I agree that 6-8 puffers would be too many for a 10 gallon.
I'd put no more that 4.
I've also read several times that they need to be in a species only tank.
I think 1 blue ram and 3-4 of the smaller varieties of cory's would be good.
But keep in mind the cory's would always stay on the bottom, so the tank might look a little empty with only 1 Blue ram in there with them.
Maybe a small school of a type of tetra with 3 cory's?
You need to have at least 5 neon tetras in a tank. They are much happier with higher numbers. How about put the neons in the new tank, add at least 3 more and the 3 cories? And then add some tank mates for the fish in your other tank?
Most, but not all, fish would prefer to not be the only one of their kind in a tank.