Fate and the Fate point economy is all about Aspects. Short of houseruling something, you're stuck with that, sorry.
The character's aspects are not the only ones in existence, though.
The SRD states
Just like with every other kind of aspect use, you can use situation aspects (and by extension, game aspects) for compels. Because situation aspects are usually external to characters, you’re almost always looking at event-based compels rather than decision-based ones. The character or characters affected get a fate point for the compel.
So try and use that. Don't hesitate to multiply aspects (though you should find a way to keep score) for you and the players to invoke or compel (players can also compel against themselves, always good to remember). Especially in XCom style situations of tactical play where parameters are myriad.
In short, you're over-thinking it.
If I personally were to have to model this power, I'd make a new skill (dependent on the stunt as you've indicated) and call it a day. But since you don't want to do that, then yes, I feel that Will is your best bet. I don't feel that using it for a stunt is overpowered, because a lot of stunts rely on allowing you to use skills in place of other skills, and what you've described thus far is almost exactly like Zird's example Lore-based magic in the Core rulebook.
If you really need to limit the usage of the power, though (which, thematically isn't a bad idea) I wouldn't use Fate Points; it doesn't make sense, narratively, that you can only cast a spell when dramatically appropriate. I'd add a third stress track for magic, or simply have usage of the power cause Mental stress on a failed activation roll (for which I would still probably use Will).
The thing about skills in Fate is that you can pretty much use any skill to bullish!t your way through any situation as long as it makes narrative sense; an Advantage created with Stealth is no different, mechanically, than an Advantage created with Fight, and if the Stealth character has the Backstab stunt then he's using Stealth for combat anyway. Skills are broadly applicable, in other words, and Stunts allow them to be even more so. A clever player can figure out ways to use their good skills pretty much anywhere.
So yeah, in short; make it a skill, use Will, and if you need to limit it then cause mental stress either unconditionally or on a failed roll. It really shouldn't be a problem and going beyond that is probably just hamstringing the player.
Best Answer
Consider it a self-compel
Although concession does give you greater control over your fate, you're still losing--and you're choosing to lose when you still have a chance of winning.
That means if the dice are rolled and you're taken out, you can't call backsies. If you're not taken out yet, it's possible to still win.
By conceding, you're forfeiting the chance to win, and that's pretty much a self-compel. And you get extra points for the consequences you got in the conflict as if each one had been compelled, because "[y]ou can think of this as a compel of each aspect taken in the conflict[....] [T]he assumption is that those consequences directly contributed to the character’s defeat." (DFRPG Your Story 206)
Consider it a drama bribe
The idea driving Fate storytelling is that every time something happens to complicate your life, you get game currency which you can spend to make your life easier later. Fate Core is very up-front about the fact that the Fate point economy drives this cycle of crisis and victory.
Conceding is still losing, and you should always negotiate a concession until it has a dramatic bite to it, like any other compel. Concession Fate points are a way of encouraging crisis while simultaneously providing the tools for future victory--again, just like any other compel or invocation. It's the way the engine powers the story.
It means your villain can usually escape to plot another day
NPCs can concede too! And should, often, if they're smart and have a sense of self-preservation. It gives the players a sense of accomplishment (because they achieved whatever goal they had when they entered the conflict) but sets up the villain as canny and positioned to wreak more havoc because of his fistful of Fate points.
Consider it an opportunity for the GM to do less work
Hey, my player's gonna tell me how he gets shafted instead of my having to come up with it. Awesome. I'll throw him a couple FP in appreciation.
Why do you want to discourage concession?
Concession is a pretty shiny mechanic, and although Fate is very flexible about many things, discouraging players from being able to cash in their cards when they walked into too much trouble is going to make them more cautious than the "proactive, dramatic, competent" characters Fate wants to tell stories about.
Allowing concessions is a frontline weapon in the war against ten-foot pole paranoia and the boring, time-wasting practices that come with such paranoia.
Come on into chat when you have the rep and we'll talk about what your underlying goals and motives are for discouraging concession. Probably we can work out some other way to satisfy your motives.