Good stuff being discussed here!
Fighters are really annoying having high damage weapons with low RoF. It makes shields useless against them, even though shields are really useful against our pirate fighters until they pack good missiles.
The lack of heavy weapon slots is also very annoying. There is a big gap at the beginning, then you get a few weapons that have potential midgame, then another gap when you're locked behind one gun (boomgun) for progress. The early gap makes ships like the swordfish useless since there's nothing good to put on it.
My fix would be to simply allow light weapons to be installed into heavy slots. If you can fit a big gun, why wouldn't you be able to fit a light one if that's all you have? Sure, having a battleship with only machine guns as weapons looks stupid, but it looks less stupid than with no gun whatsoever. In my current game, I'd happily put plasma spitters on my Dragons, because they're better than anything I own for heavy weapons against the targets I want the Dragons to tackle.
An alternative would be a "duct tape 2-3 light weapons together to make a heavy one" idea, which would increase rate of fire by 2-3, but also decrease accuracy, same damage, same ammo. In fact, now that I think of it, I think I'll mod that one before I play next time.