Fate has a much more narrative approach, less GM authority, and player-based plot control mechanisms. This can make for trouble transitioning from a more adversarial GMing environment.
Fate Core (and other recent Fate games such as Dresden) actually do a pretty good job of providing a suggested "menu" of powers and stunts for players to take; show them to your players and let those inform other stunt ideas through play, rather than trying to get the characters completely nailed down in advance the way you would have to in D&D.
To address the specific problems you mentioned:
The "blind sniper" problem is that in Fate, it's very easy for a cooperative party to stack multiple temporary aspect bonuses on a situation, then tag them all for a single super-successful roll regardless of innate skill.
Consider a sniper with a base skill of +0 - "has no idea what he's doing". First he hides on high ground (creating aspect "On a Grassy Knoll"). One of the other players - a tech - has made, and gives him some "Precision Armour Piercing Ammo", with suitable aspect. Then another player jumps into the road to stall the target into "Standing Still for a minute", so the sniper can create advantage by taking an acting to put him "Centred In My Sights".
Then the sniper free-tags all of those, for a base roll of +8 and a near-certain hit - with fate points to spare if he needs them.
Stacking enough of this sort of this can greatly reduce plausibility, but it's obvious behaviour for a group of D&D players where it's an expected part of the system to need to stack every combat advantage you can generate. I don't, however, feel it's as much of a problem as some Fate players do - this is behaves-as-designed. Fate characters are supposed to be able to beat pretty much any single obstacle if they can generate a convincing narrative. "He's not that good a shot, but it worked because an entire team was helping him take it" is a pretty good narrative to me, and gives the plot and characters room to develop further.
The "constant compels" problem arises when GM and players get caught in a Fate-point loop of constantly compelling aspects to force behaviour or non-actions from each other.
Remind your players, and remember as GM, that the point of compels is to implement narrative development. The Fate point economy will naturally limit how far players can push this, so it's not a problem unless the GM gets sucked into constantly offering Fate for compels. So don't. Compel when it's a narrative or character development to do so, not just because it's possible.
Long combats occur because groups have trouble actually taking out opponents of similar skill levels. This is particularly likely if your group is used to D&D, and trying to "wear them out" by all attacking individually. In Fate it's much more effective to set up a narrative about a couple of major attacks, taking multiple actions to support each other and make those go off well.
The best counter to most of these issues is threefold:
Let them have their moment. Players being able to tear through obstacles like this is not a problem in Fate the way it would be in D&D; it's expected behaviour of the system. Don't make it impossible, but ask what happens next and generate new obstacles. The problem can come more from a D&D-oriented GM feeling he has to make tasks "possible to fail" than from actual issues.
Your enemies are not idle. Don't GM in direct opposition to the player's actions, but instead change the game. Fate uses the same mechanics for social and combat conflicts, and it does so for good reason, expecting them to intermingle. Use it. Enemies will attack on social fronts, run away if they're in trouble, consult allies, adjust schemes, and all the other narrative options that are not often available to an orc in a dungeon.
Remember that in Fate, the player is always an informed participant, even when the character isn't. The gap between player and character knowledge is much bigger in Fate.
Situation: A hostage is tied to a chair. There is a trap which incinerates the room if anyone touches the hostage.
D&D answer: Tell the players nothing. Make hidden Perception checks. If anyone explicitly searches, make Search checks. Lie unless the players succeed at these checks.
Fate answer: Tell the players immediately that there's a trap. Let them make rolls and use aspects freely to see if the characters spot it. If one of the players has a "reckless" or "rescuer" aspect, compel it - offering a fate point if their character runs in carelessly and sets the trap off. Make the players partners in decisions that hurt their characters.
Fate Worlds: Kriegszeppelin Valkyrie
You might find what you want in Fate Worlds Vol.1, specifically "Kriegszeppelin Valkyrie" (KV). It is a mod/campaign where PCs are WWI pilots. Their planes are stationed on a giant flying aircraft carrier, the eponym Kriegszeppelin Valkyrie. Change "planes" to fighters and "flying aircraft carrier" to "capital ship", and you have a good start!
Now, that's probably not enough detail for you, so let's mention some rule points and how they might fit what you would like to do. I will avoid quoting extensively considering the book is not open source, but here it is.
Fighters
Fighters are represented by Stunts. Each fighter costs a given amount of Refresh (between 0 and 3) and gives specific bonuses. One fighter would for example cost 2 Refresh and grant a +2 to Pilot rolls to defend and create an advantage due to high maneuvrability. Another would cost 1 Refresh and grant Weapon: 2 once per combat due to heavy guns.
As for damage, the combination Pilot+Fighter symply uses the pilot's stress tracks as is. You could however create a separate "Piloting stress track", with additional stress boxes for higher Pilot skills.
Dogfights
Dogfights in "Kriegszeppelin Valkyrie" are handled through a simple rule. Fighters making a straight attack without first placing an advantage on their target can do no more than one stress damage, no matter their Stunts, their roll, their final result, and so on. A fighter needs to first succesfully create an advantage on their target to be able to do full damage.
Capital ships
The Valkyrie in "Kriegszeppelin Valkyrie" is treated as its own character. It has its own stress track, Aspects, Trouble, Stunts, and skills. It uses its captain's skills and stress tracks for mental attacks.
This makes sense, considering a ship with a huge crew is less dependent on its pilot's skill. Put Han Solo at the helm of a capital ship, and it probably won't be much nimbler despite his superior skills.
Other ships
"Kriegszeppelin Valkyrie" has a couple of other ships described as opponents:
- Gunship: Heavy guns and bombs
- Troopship: Transport carrier
- AA Gun: Anti-aircraft gun
- Airship: A big flying ship, but smaller than the Valkyrie.
Fate System Toolkit: Scale
You mentioned it already, but for the sake of completeness I would like to point out the Scale subsystem in the Toolkit which might help you reach what you want.
You define a number of scale steps (3 or 4). Larger entities have a number of bonuses against smaller ones. This allows you to split ships into size categories (fighters, freighters, small capital ships, big capital ships). The more categories you have, the more difficult it becomes for small ships to affect bigger ships, which might or might not fit what you have in mind.
You could change the bonuses to be more similar to Star Wars RCR: for every step separating two ships, the smaller one has bonuses to attack and defense, but the larger one has bonuses to damage and armor.
Best Answer
I'm going to create a completely system-agnostic answer here, but it will probably apply to you, especially considering the example of A Song of Ice and Fire.
The reason that characters can drop like flies, even semi-randomly, in A Song of Ice and Fire without it detracting massively from the story, is because the story isn't about them. If someone whose tale you enjoyed dies, his story generally doesn't end there. What he did in life, how he died and what he was hoping to accomplish carries on into the future, influencing other events and the actions of other characters. The specific person may die, but the struggle over who gets to sit on the Iron Throne continues. Two houses might have some more enmity between them, but both Houses live on. (Even if you kill most of its members.)
So I think if you want to have a highly lethal game, you should try to emulate that. Don't tell the story of "Bob the Wizard and Jim the Fighter Find The Magic Gizmo And Save The Kingdom", instead tell the story of "The Magic Gizmo And The Twelve Groups Of People Who Want It".
I think that you'd need a change a few things to make it work, but it might turn into a very worthwhile and different kind of campaign. I would approach it something like this:
Scrap all preconceived ideas of where the story will go
Since this story will not be about any specific characters and there will be no good or bad side, it should not have a set direction. Instead, let it flow where it will. To some, this is normal, to others, it's a chance, but I think in a game like this it's a must. What makes A Song of Ice and Fire work is that for the most part, nobody has a clue who the good guys are and where the story will end. We want that feeling.
Present a situation/object worth fighting over, without assigning good/bad sides or fixed abilties
To keep the story going, there needs to be something that generates conflict, but it has to be something that isn't hamstringed into only doing a single thing. A Gizmo that can save the world from invasion by aliens isn't a good fit here, because it only does one thing and everyone will want it for the same reason. The One Ring is roughly in the same basket. But the Iron Throne on the other hand? You can do lots of things with it. The crown to a kingdom, an artefact that gives considerable (but not absolute) magical power to the wielder, a hoard of gold of incredible value, these are good things. You need something that will make people fight for all kinds of reasons, without an outside observer immediately being able to say "this guy good, this guy bad".
Do not assign player characters. Assign players Goals.
Characters are just going to die, probably a lot. That's good, and people should still get attached to them because it makes better drama and involvement, but we don't want the character's player to slam into a wall when the dice (or another player) finish off his character.
So instead we assign players a goal and then we attach characters to that goal. So instead of Tim playing "Jim the Wizard Who Wants the Magic Gizmo To Save Someville", Tim will be playing "The People Who Want The Magic Gizmo To Save Someville" and today he will be "Jim the Wizard". Now, when Tim gets his character killed, he doesn't have to stop. In fact, during play he probably revealed numerous characters who share his player-goal and he can just jump into any of those in an instant and continue playing his Goal. He can even switch from time to time when his other character(s) are temporarily out of the spotlight.
Give your players a reason to work with the goals of other players
The next step is to make sure that play won't devolve into each player running around on their own. You need to make sure they intertwine their goals, or at least make it so that their characters think their goals are intertwined, so they work together. (Until the inevitable backstab, of course.)
For example, the goals of "Use the Gizmo to control the people of Kingdom A" and "Use the Gizmo to prevent a war between Kingdom A and Kingdom B" are not exclusive to each other and people fighting for these goals could very well align (even if one is a little darker than the other).
Sometimes, even the simple threat of an outside Goal that interferes with both can be enough to get a group to work together for a while. (And it'll generate loads of conflict because both sides know it's temporary and they don't like each other). If the NPC party of "Use The Gizmo To Plunge The World Into Darkness" is clearly winning, maybe even "Use The Gizmo To Subjugate Kingdom A" and "Use The Gizmo To Bring Glory To Kingdom A" might work together for a few days.
And finally: Don't let characters hold back
Since the setting has to be lethal and we've set up the entire story to not be about specific characters but about a source of power and the struggle for it, characters can die freely without blocking anything. So make sure they do. While in most games, one player's character backstabbing another's would grind most of the story to a halt, this one is set up for it to not be a big deal, so make it not a big deal. (Give them a cookie every time they pull it off or something.)
Since the players are running a Goal, losing a person dedicated to it is probably not a very big deal. (For the progress of the story and the player's ability to play. It might be a very big deal for the goal and the other characters, but that's a good thing. Drama!)
The only thing that would truly disrupt a player's ability to play would be the complete and utter destruction of everyone who is trying to accomplish his goal... but that requires so much scheming, plotting and interesting storytelling that A) you'll see it coming from miles away and have plenty of time to flesh out a new goal and B) it would be awesome