One can create a nice, small and robust 29-30 knots CV (NOT CVL, heavier then 16000 tons) that can carries 36-40 planes (depends on how much armaments, torpedo protection and armor you put on it) with 1950 tech. Building 9 of such CVs, load them with fighters and torpedo bombers and then deploy them in triplets, you got a very nice carrier forces that can provide basic CAP and strike capacity, acting as force multiplier for the capital ships and allow them to fight the larger enemy fleet, esp. when the land-based planes provide recon.US.
I was also limited by a 12 year Treaty that limited ship size to 18000 tons. Also the ships there were meant to flee to the Pacific afterwards to beef up the Philippines
The current AI remains pretty bad in carrier warfare and I have negated enemy's numerical superiority in capital ships by using CVs/CVLs. Also, I tend to design my capital ships with heavier armor and comparable or faster speed while compromising on firepower, so my ships are generally more survivable than AI designs and rely on training and good fire control to hit first and hit accurately.