I have researched this subject quite abit, and here are my thoughts/experiences:
Peppermint shrimp I purchased 3 and they cleared 1 rock's worth of Aiptasia then stopped wasn't even 10% of my population at the time.... Then they ate every feather duster I had in the tank, then pretty much just ate left over flake etc at night, And then my wrasse found them...I would never try these again, also there are multiple species that are sold as peppermint shrimp(look exactly the same), but are not; these species will not eat Aiptasia.
The Naudibranchs: I heard do extremely well, but there are several draw backs. They are expensive for as finicky as they are. They are picked on by just about anything in your tank(not just wrasse...crabs/shrimp will aswell). And since they only eat aiptasia, once it is gone they will be too unless you add more aiptasia.... I think the best and most common approach to ridding aiptasia this way is to put them in a separate tank and allow them to do their magic on a few rocks at a time. Most people will give them away or sell after they have cleaned the rocks and have no more food.
Chemicals: Waste of time IMO and experience... I know alot of people swear by them... but everyone that I talk to that does; still has aiptasia, or did not have a large established colony of them. IT appears to work great the first few weeks and then right around week 3 or 4 you notice you made a HUGE mistake and my colonies were easily doubling in size and population. I WOULD NEVER DO THIS AGAIN.
Klein's Butterflyfish THIS WAS MY HOLY GRAIL! I was at the end of the road in my war with my huge aiptasia problem, and was ready to yank the whole tank apart and restart after acid bathing the rocks. I did not want to do a CopperBand as they are not very hardy and are specialised eaters, My water's perimeters were all out of whack and I could not see risking 60 bucks on a fish that more than likely would die from my tank before ever doing the only job i wanted him for. Reefchik had suggested a Klein's butterfly as a more suitable replacement, She stated she has always had one and never had a single aiptasia ever since introducing him to her tank... AND I COULD NOT AGREE ANY MORE! I put mine in the tank and he was a pig, he started working his magic the next day, within a week it was very clear I had made the correct decision. He had cleaned my colony of 100+ within 2.5 weeks, and I have yet to notice a single aiptasia come back since. And as you know he died a week ago... They also are not specialized eaters like CBB, mine ate anything that didn't eat him first, he was real good on flake and frozen food. And I know they are not the most reef safe solution, however after the aiptasia were gone I only ever noticed mine picking at my xenia, and he didn't eat the whole thing he only ate the very tips(rich says his do that as well and he has never experienced any negative affects on the Xenia, and he has a ton)..... I WOULDN'T HESITATE TO BUY ANOTHER AT FIRST SIGN OF AIPTASIA, GREAT FISH... I would highly recommend this fish for you, also when he is done you can easily transfer him to someone Else's tank to clean theirs.