[Will]

Yeah, in the stock game, pretty much the only time you'll use carriers is if you get Fighters I before you get higher levels of ship construction. Light Carrier can have a few Heavy Mount weapons when it has the minimum cargo requirement, and they're useful to have a few big guns early to complement the smaller ones. But overall, fighters are far too weak to use it throughout the game.

And for your story, you might want to adjust the number of pilots on each carrier, and then the number of crew accordingly. I think your bombers are two-seat affairs, and your fighters are single-seat craft, leaving you with exactly the number of bodies to fill all the fighters. In practice, you would have MORE pilots than fighters, mainly for the reason of always having a good number of pilots on alert at all times (they have to sleep too, you know), and because the health of the pilots isn't always guaranteed (launching a planetary assult? You better make sure none of your pilots gets the flu before, unless you're willing to field fewer fighters).