This is the problem at a fundamental level.
1) Carriers provide strong offense (weapons that scale automatically with tech).
2) Carriers provide strong defense (free hp every combat).
This is better than anything a single weapon or defense module can provide, and as such...OP.
If carriers remain mechanically as they are, then balance requires a strong nerf. Their offense would have to be lower than any weapon at the same tech level by mass...period. But that method of balancing is difficult, because fundamentally carriers are in direct competition with weapon/defense modules, and its very easy to make one strictly better than the other.
That is why I agree with several of the suggestions in this thread, that the best balance is to make carriers DIFFERENT from weapons/defense modules.
This would include suggestions made in the thread like:
1) Require resources (maybe 2 different types of resources).
2) Heavy maintenance cost.
3) Has to go to planet, starbase to "restock" fighters.
I ultimately think that is the best way to balance, just tweaking the numbers will make balance very difficult.