Just be aware that bigger battle size means the enemy can deploy more forces at once as well. It can help, but isn't guaranteed.
It seems like you have the basics down so improvements are going to start being harder, especially as you don't pilot. Fine tuning builds is part of improving combat performance, as is overall fleet composition. I personally do not like cruisers very much for endgame and prefer capitals + frigates and/or destroyers depending on tech level and build (low tech doesn't use frigates, mid tech likes unofficered tough filler frigates + destroyers, high tech might not use destroyers because their frigates are so good and benefit from wolfpack so much and might use their destroyers as unofficered ships rather than their frigates). For me the reason is that, in general, cruisers have a lower ratio of offense/DP than the other ship classes, the truly offensive cruisers do much better in player hands and at that stage capitals are a better player amplifier, the 'anchor' role is better done by capitals, and there is a lot of value in just having more ships on the board than the enemy (or at least not be outnumbered so badly!).
Oh, and if you aren't using lots of missiles: use lots of missiles.
The last part really made me laugh! Yes, all my officers have the 2x missiles trait, and I do focus on missile spam as I can. The preceding info on fleet comp made me think. I read quite a few posts indicating the meta was faster/smaller ships in the current build, though my experience in game was leading me to your conclusions - capital ships are king and cruisers for the most part just can't do much compared to Capitals, besides using their long range beam weapons to discourage blobs from overwhelming your capital ships. I also believe the AI is good at many things, though escort pathing is awful. I've watched escorts time and again either rush out in front of the capital, only to be focused and die, or get stuck behind the capital, unable to contribute. Cruisers do seem to escort each other quite well, and I do like to put two Apogees together. Capital ship escort is where things devolve, from my limited experience at least.
BTW, just noticed below your sig, "Harpoon Fan." Are you referring to the predecessor of the Command line? If so, I'm right there with you. I played the entire line from the original Harpoon game, though Harpoon 97, to the Gold Edition and now own all the Command releases though I've slowed quite a bit with the latter. Command has been plagued by bugs which is a deterrent since my game time is quite limited. It does appear to have more support the last year or so than I've seen previously, which is a good thing.
Thanks again! I've got quite a bit more learning to do about this game and maybe a change in my fleet comp once I find more blueprints. Exploration!