There are two ways to make your cap ships lvl quicker.
1) Raise the XP values of each ship and building. Look for a line in the .entity files that looks like this:
experiencePointsForDestroying 7.500000
2) Go into your Gameplay.constants file and look for the "CapitalShipData" section. BTW, I assume that this is where you can add in additional lvls to Cap Ships, but I haven't tested it yet.
And since I'm on a helpful trip here's yours Red:
Find this section in the PLANTEDMODULE_PSI
Thanks. But thats what Ive been doing.

It doesnt seem to work at all though... It worked fine for the TEC, everything I modded including ships and structures worked just fine. But for the Advent, only the ships I mod work ingame, and not the structures.
It weird, im doing the same thing for the Advent/PSI that I did with the TEC/Tech.