+1 on *not* doing a copper treatment. Why poison your tank, potentially rendering it lethal to the stuff you want to keep, if there are other options?
Manual removal, done regularly and persistently, will go a long ways to getting rid of the problem. If you've got floaters, they're an easy place to find 'em. If you don't--do a light prune and let the trimmings float on the surface--pond snails will tend to congregrate on 'em, making the critters easy to find and pull.
Meanwhile, ease back on your feeding and do a good clean of any dead or decaying plant material. And then get yourself a single assassin. Takes two of 'em to reproduce so a singleton won't put you at risk of a new snail problem, and a singleton is pretty unlikely to tackle a nerite. The assassin will be able to reach the areas you can't even see, much less reach.