Apogee is not really a ship that can kill. Unless we're talking some meme SO build with autopulse+AM blasters+hurric, of course. Plasma is kinda bad here because it will miss 90% shots on anything smaller/faster than Hammerhead. Tachyon cannot deal any hard flux, and you have no missiles or ballistics to help out.
Why do you say it has no missiles to help when you mention its large missile in your loadout (it has a small missile as well)...?
Plasma cannon is the only good build IMO, but it is certainly a good build. Hitting frigates is not important, it will deal good damage to destroyers/cruisers/capitals which is way more valuable. Using locust in the large missile slot and giving it an escort is more than enough to fend off harassing frigates. It will absolutely win duels against cruisers that cost 50% more DP. I consider plasma apogee to be the some of the best value/DP in the game. Other loadouts are considerably weaker, but it still has amazing campaign stats that are worthwhile in any case.
My build:
Plasma cannon, burst PD (small) in the medium slots, small energy slots empty (I might have a third busrt PD somewhere), locust and small sabot in the missile slots, hardened shields, max dissipation, ITU, stabilized shields, and probably some caps or maybe another hullmod or two, I don't remember exactly.