there is a new mode in the game where you have a Executor as your starbase, but otherwise those are not indended for skirmish, since they cause problems as you've experienced. (I think)

Oh wow, I was completely unaware of that game mode. And I appreciate the effort but man what a buggy mess. I could barely run for 5 mins. Although, I suspsect part of that has to do with the additional features of that mode.. Being able to just spawn in whatever you want basically on command has to complicate things for the engine somewhat. Especially if they're massive ships.

My biggest reason for wanting the supercapitals is just to balance out skirmish a bit. it seems like once you reach tech 5, the New Republic just has absolutely crazy powerful vessels, especially via the heroes, and the other factions lack quite a bit

If you want lots of Dreadnoughts there is also the Instant-action mode, forgot to mention this.
There you can build every SSD and also multiple of each without popcap or techlevels.

Simple solution. Rush the New Republic. Don't let them reach tech 5. That's what the empire should have done. Got their ♥♥♥♥ together, stopped fighting each other, and rushed the rebel scum.

Well its not so much that I have difficulty, as the AI rarely builds heroes unless the space port is directly in the center of the map where they like to congregate, but I enjoy the "bigger fish" aspect of the mod. Fun to have a bigger ship replace a smaller ship which replaced a smaller ship etc. Having one more layer of ships would be cool, especially for the faction that built the largest, most prolific ones