I would go with assassin snails as well. When I was really new and dumb at this(not saying newbies are dumb lol) I bought a couple of clown loaches to help. Well I went to a fish store and saw an adult clown loach and though GEEZ that is a big boy. Well, I do not have a tank to accomadate that much fish, so even though I enjoyed those loaches, as they were really neat to watch, I had to rehome them. They were only about 2 inches long at the time I rehomed them, but long story short, I bought fish to solve a problem and ended up with more that I would be able to handle in the future. If you cannot get assasin snails, I finally got rid of the problem when I moved tanks. I was able to rinse everything out and let it dry, so of course the snails died and problem was solved.
Now please someone correct me if I am wrong with this advise. If your tank is cycled completely, what you could potentially do is put some of your current tank water in a large bucket with the filter, and empty your tank. Rinse the gravel really with hot water to rid of snail eggs, (you may want to rinse out your filter but take your media out first so the warm tap water doesnt kill your bioload.) and rinse all of your ornaments and the tank itself. This should kill all snail and when you readd water and dechlorinate, your still have your media so your tank will be cycled, and your problem will be solved. The only thing I am think though, is that is a 100% water change almost and I may be thinking way out in left field on this idea. Unless you have a bucket to accomadate 50% of your tank water.....
Please someone correct me if this is bad advice.