I second the assassin snail idea. I had a severe infestation of trumpet snails. I introduced three assassin snails, and within about three months the trumpet snails were eradicated. Completely gone. Assassins won't overpopulate either.
By the way, I have couple opinions/experiences that differ from the common wisdom. First, keeping snail numbers manageable is not as simple as "don't overfeed." In my Sumatra biotope, I fed extremely sparingly, and yet the trumpet snails continued to breed out of control. I don't know what they were eating, but it wasn't fish food. (I should note that the tank had a soil substrate, which certainly added nutrients to the system).
Regarding the "don't ever buy a fish to do a job" mentality, I get that too, but I have a slightly different view. To me, an excess in a tank is often a resource that isn't being used, and it's kind of fun introducing a species that will be able to use it (assuming, of course, that there is a species that will do so, and said species will be compatible with my setup, water, and other residents). In my hillstream tank, I am intentionally cultivating algae and biofilm with excess light, for future hillstream loaches to enjoy. When I see snails overbreeding, sure, I'll try reducing feeding. But I'm also thinking, "Wow, some assassin snails would LOVE this!"