Maybe the inherent Carrier defense value should be boosted, to compensate for the weaker fighter. Let say you can land 2 planes on the Carrier, but the Carrier itself has a little fighter force just to close combat self defense, making the carrier defend on D3 ?
Very good idea: it is a can opener. It gives much room to compensate.
Maybe you can even give it the classic A1D3, if necessary for balance.
Or even going that far: A2D3, so almost all of the OOB A3D4 Fg + A0D2 Cv= A3D6, will be converted: Fg A1D2 + CV A2D3 = A3D5.
Just suppose that there is a bunch of escorting ship/fighters wich can not be separated from the Carrier unit.
It can probably solve a lot of balance problem.