For me, the only suggestion I have pulls back focus a bit- keep the relatively rock/paper/scissors relationship- perhaps even simplify it and focus it. BUT two things:
1: TIE weapon types even more strongly to their particular resources required to build them. Only weaker versions require no special resources.
2: The counter defense for each weapon type is NOT tied to the same resource as it is now (Elerium for lasers/shields) but to another.
Lasers and Armor (Anti Kinetics): Elerium
Missiles and Shields (Anti laser): Antimatter
Kinetics and Flak (Anti Missile): Durantium
or put another way:
This would bring the strategic world of the game down into the tactical outfitting of your ships, and allow you to read the map (resources which race has) and make tactical plans based on your strategic situation.
I'm thinking that definitively changing the tactical combat itself is a near impossible task without losing the strategic input Brad clearly wants tactical combat to have been derived from.