Is there a reason you don't want trumpets? I know they have a bad rep but I personally see them as a necessity at this point. They mostly hide in the sand when all is good in my tank (moving around and preventing anaerobic pockets), and the sudden appearance of more of them kindly signals tank attention (uneaten food that went undetected, something else I need to attend to, etc). I have hundreds because it's been a few years and I make a point of keeping them (mostly hidden, when I clean the water/substrate I try to put them back) and have never noticed a substantial bioload increase. I'm sure they are making one, but I think they are probably canceling it out by cleaning and ingesting algae and larger snails' waste.
Also, from my experience with puffers, your population will have no problem staying under control. It's also been suggested to me by a marine biologist friend that they need a substantial amount of snails to stay alive.
Even if you find another alternative, you need to feed your buddy a few snails on a very regular basis. He needs it for his teeth.