Filthy tanks are feasts for snails. Don't let the water quality turn downright toxic, but give them as much food as possible. I don't mean just overfeed fish food, but also crank up the lights, and add things like leaf litter and driftwood. Heck, maybe even put it in direct sunlight. Make it so that any snail, no matter where it is in the tank or how small it is, will always have plenty of algae, biofilm, and decaying matter to munch on.
Oh, and be sure to keep the pH pretty high and feed/supplement lots of calcium to optimize shell development. Holey rock and other limestoney rocks are great for this.
Also stick with pond, bladder, or malaysian trumpet snails. I've found that ramshorns don't breed fast enough to be a consistent feeder snail.