It's generally not a good idea to intruduce fish just to solve a problem...
Assassin snails might not be so bad, but assassin snails work slowly... They breed slow, and only eat about 1 snail a day. (Pond and Ramshorn can reproduce faster than that.)
I would cut down on the feeding- don't let any food touch the substrate (unless you have bottom feeders...)
You can also get a thin slice of cucumber or zuchinni, freeze it solid, and weigh it down in the tank right before lights out. In the morning, you'll have a pile of snails on it and you can throw them in the garbage or something.