My first inclination was to recommend yo-yo loaches if this was a thread asking how to get rid of those pesky snails. Now that I see you want them gone, I am STILL going to recommend yo-yo loaches as I have experienced what they can do first hand. My tank was severely overrun back when I was about 12-13 years old and would overfeed my fish. I was throwing away 75 snails in the morning and at night each day (29g tank) for 10 days before I decided to add these loaches. I added 2 after doing one final cleaning where I removed 250+ snails. There were still many more snails that I didn't remove because I wanted to see if they would do their job. And boy did they! In 3 days not a SINGLE SNAIL was crawling on the glass of the aquarium and the bottom was littered with empty shells. They work spectacularly and these aren't a fish that will impact much else in the aquarium. They are good with all types of fish and they stay on the bottom of the tank. I disagree with adding something else to solve a problem because of this perfect example. It's MUCH easier to remove 2 loaches one time than it is to remove countless dozens of snails each day. I don't think that they would eat your larger snails, but just as a precaution I would home them in a gallon milk jug or another tank until the loaches do their job. Then add one to the tank and see how the loaches react to it before deciding whether or not to add the others. You can always get rid of the loaches when you are done with them, but I have a feeling you will like them and will want to keep them.
I don't recommend assassin snails because they don't reproduce fast enough to make it worthwhile. And they will only reproduce when they have other snails to feed on, so you don't have to worry about their population getting out of control. That is one of their benefits.