I would bump up your current tetras to 6 of each of the two kinds. They probably seem to be schooling together because it's a fairly small tank, so the true schooling behavior might not be coming through. They tend to just use the whole tank and interact with each other but not really school. Plus, the limited numbers for the school are probably making them insecure so that they are schooling with fish they wouldn't normally school with.
I would go with a honey gourami instead if you want to add a gourami. They are more peaceful and would still fit in a 20g with the rest of your fish.
I would go with a honey gourami instead if you want to add a gourami. They are more peaceful and would still fit in a 20g with the rest of your fish.