You'll have to watch that aggression between the rams and be prepared to have to pull one or two if they are not compatible. You never know who's going to be the bully. Also, if a male and female pair up, you might have trouble with them ganging up on the "third wheel" and also possibly harassing the other tank mates when breeding. I never had rams breed (only had a single male and then two supposedly females that died within a month
so never got to see breeding action); however, I did have kribs that I had been recommended should be fine in a 75g community, even when breeding, that killed 10 diamond tetras defending their babies. Cichlids are excellent parents, but they are not the best for community tanks when breeding. I would either watch them like a hawk and pull at the first sign of aggresion if breeding or just go with 2 females. I'm not saying it's impossible, but I am saying that you should be cautious.
Otherwise, the cories should be fine with rams, as should the tetras and dwarf rainbows that you mentioned. The only issue that might pop up is aggression from the rams when they are defending their babies.