If it were me, I would hammer the green carp, getting their numbers in check before adding any panfish. I'm afraid that unless your BG or RES are bonafide six inchers, if your pond is really overpopulated with bass, you'll either lose most of them to depredation, or their progeny just won't make a huge difference if pounded by both the preexisting predators and their YOY this spring/summer.

I haven't had much luck overcoming the "green carp scourge" by stocking/overstocking alone-got to get those predator numbers down.

That doesn't answer your question, however. If your main goal with the additional fish is to increase forage, then add the BG, they'll spawn several times this spring/summer. If your primary purpose is to increase diversity, then by all means add the the RES, they'll do great in NC.