Try using a long range weapon on your carrier and some short range weapons. I am no 100% certain but my carriers seem to deploy their fighters and bombers as soon as my giga canon can fire and they can defend themselves with their gauss weapons/ matter disintegrators when ships gets close while the fighters are busy or dead. I usally win even against fleets with superior fleetpower from fallen empires or the unbidden.I think combat range mechanics is the issue. You should be able to tell your fleet to attack a target from the other end of the solar system with fighters/bombers without moving "in range" with your other weapons.
Right now, even if you give your carriers 120km engagement range (mod) they'll still wait to engage until their conventional weapons are in range. It seems to ignore the near infinite(?) range of fighters and bombers.