I'm going to go against the grain here on the Copperband idea, while GREAT Aiptasia killers, it's VERY VERY hard to get a healthy one, not to mention one that will eat prepared foods after the Aiptasia are gone. It seems senseless to me to keep killing these fish in hopes of trying to find a healthy one that will also eat prepared foods.
I'm going out on a limb here....but here are some reasons why the methods you've tried already are not working.
Peppermints, depending on how much you feed the tank, they learn to take prepared food and will wait for it instead of eating the nuisance aiptaisa. Also depending on the size of your tank and how bad your infestation is, 2 may not be enough to wipe them out, they may be reproducing more than the shrimp can eat.
I've never tried filefish, but I would tend to guess they will act the same.
A third option are Berghia Nudibranchs. I've not tried them personally because my trigger would have them for lunch, but it's another option.
I'll be honest here, I'm about in the same boat as you, but worse off because of my trigger would eat any natural methods of ridding myself of aiptaisa short of a copperband, which I refuse to try again. I'll soon me stripping my tank of all my large fish, beef up my clean up crew with more peppermints and a nudi or two, and see how things go. I would hate to see you leave the reefing scene just because of aiptasia.