I don't think you have to hide the numbers for what you are doing, but rather just how you get them.
I've made my game more player facing, i.e. they players roll all of the dice. But I've also made it more narratively driven, i.e. the players don't invoke their powers, instead, they describe their actions. (Taken liberally from *World games)
I did this in response to exactly the problem that you're having- that DFRPG can be overwhelming at times. So how does this work?
The first part about the GM not rolling takes a lot off of the GM's shoulders, and makes things faster. You then use this savings to spend the time to interpret the players' actions, and trigger them based on the narrative for the players that are less familiar with the rules. Rotes help a lot with this.
So, the only things you have to explain to your player are- the rotes that you help them design with their characters, and the meaning of overcasting vs standard casting. Once you've done that, the player describes what they are doing, i.e. casting their rote, or putting more effort into it or really pushing themselves. You look at the numbers behind the scene, and give them the target. They roll... and describe what they are doing to invoke their aspects as needed, since they know what they need to make the roll.
This way, they are eased into the aspects of the game that have to do with Fate, while the crunchy things of magical manipulation are kept behind the scenes.
In summary, let them describe it in the narrative, you do the heavy lifting, then let them roll against a static number, invoking aspects as needed to make the roll if they want to so with more narration.
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
Write out a starter set of "power cards" on index cards, formatted somewhat like the D&D 4e power cards for familiarity. They can have some normal FATE combat options, and also some tailored to her Aspects - you can make these up yourself, or based on things you've heard her say she'd think her character could do.
After each combat, tell he she "leveled" and give her a blank card to write a new power of her own design on (help for the first couple times). Eventually as she gets more and more and realizes that she is making them up anyway, it'll wean her off them. The second she asks "can I do this, it's not on a card..." you say "Yes!" and think "Hallelujah!"
I will note for posterity that this isn't ideal - ideally the player would catch on to the world of more freewheeling roleplaying without requiring this. But if they've been mentally scarred by restrictive games to the point where they're just not catching on and need structure, which is the scenario the OP presents, then this can work.