Giving carriers 4 heavy slots and turning them into battleships sounds like giving up on the class to me.
Perhaps light carriers could receive 1 heavy slot and 5 primaries while heavy carriers receive 2 heavy slots and 6 primaries, along with appropriate core upgrades. Medium carriers would have 1 heavy slot and 6 primaries or 2 heavy slots and 5 primaries.
That is, assuming they don't receive the buff to secondaries and a very slight thrust (or have their impulse speed increased to 100 m/s). Giving them heavies AND doing that, could turn out to be overpowered.
They could also perhaps be given a second drone. I know people are worried about the possibility of people using a dozen carriers and having two dozen drones, but I really don't expect that to happen often, as they would be left extremely vulnerable to battleships.
