I had a really aggressive outbreak once. Judging from the reports on R2R of various people and my own experience, I believe (but obviously don't know) that there are different species or strains involved. Some can be easily dealt with by using the various products to dissolve aiptasia, but others (mine included) just take this as an invitation to spread even more.
I tried peppermint shrimps first. They did only irritate the aiptasia whenever they catched some food, but didn't really eat them. Then I got rid of the peppermint shrimp so I could add Berghia nudis. Unfortunately something else in my tank ate those (I suspect the hermit crabs). In the end my copperband butterflyfish saved the tank. You will probably never get all aiptasia anemones and if you don't want to spread them, I recommend only cleaning things that you can fully take out of the tank and soak in bleach or acid. A little bit of pedal tissue is enough for them to spread.
For the few my copperband can't reach I'm currently using Aip-Away which appears to be far more corrosive than AiptasiaX. After 20minutes I take a small tube and siphon out all residues which reduces the amount of product that is floating through the tank and it might get a few cells that haven't fully dissolved yet. Only then the flow is turned back on.