I find it interesting that we all have had different levels of success with the standard fixes. My experience on this subject goes back a long time. I battled aiptasia in the late '80's and early 1990's when little was known about natural predators. I was a young guy who read all he could to try to solve the problem. Every tank that tried to keep corals had aiptasia at some level. CBBF's were the preffered method for extermination for those with big tanks and a lot of fish keeping expertise.
Kalk paste and the other chemical methods seemed the best for the rest of us but, you could never get them all. There were always some behind rocks and other places where you could not get at them. You could keep the population low with these methods but never exterminate them completely.
Then the mystery of the several different species of "peppermint shrimp" was solved. Although two species do eat them, IME only one species is truly effective: L. wurdemanni. The others look almost exactly the same. I have cleared four or more tanks with these shrimp. They do not attack anything that I know of (tube worms, small feather dusters, clams, SPS, Softies, are all safe - of course there are always exceptions). The only issue is that they have been known to rip at a LPS to get a piece of food from it and can do damage in the process.
The other key to success is to not have a lot of other food for the shrimps. If fish food ever hits the sand in your tank, these guys will find it and get used to eating it. If they are hungry they will eat aiptasia. In most reefs they will get enough to stay alive by scavenging at night but will still be hungry enough to clear your tank forever.
Just my experience,
John