Man if you are able to successfully cycle a small tank using neon tetras, you should be giving the experts advice.
Don't apologize for cycling your tank the old school way. Most use tougher fish to cycle a new tank like barbs or zebra fish.
Don't be shocked if you lose some neons.They are fragile and relatively short lived even in the best situations.
might be pushing your luck adding more neon tetras. Maybe add a few zebra fish to complete the cycle, and add a little extra movement to the tank. Good luck.