Yea i would say you could do it,cause just getting pairs to form will take a while so i think that there wont be that much aggression.You never know unless you go for it.
I'd advise against rummynose tetras(2-3" long where I work). They get largeer than your normal tetras and are more active. I would say get either Cardinals or Lemon Tetras. I dont see a problem with having Neons with them as we have Neons with Rams at wrok. I just wont get a pair unless you want to keep them by themselves .
2 GBR pairs in the same tank probably wouldn't end up well. 1 GBR pair and a few small schooling fish (small tetras, rasboras) and a few otos for algae.