I know this post is late as I see you've already pulled the rock and killed it but maybe it can help somebody in the future. You can win the battle but you have to be committed and diligent in the fight. I had some rocks and frags I wanted to keep but they had aiptasia on them. I have them separated in a QT tank. I sit in front of the tank and inspect all the surfaces looking for their ugly little heads poking out from any nook, cranny, holes, creases, ECT. If I see them I pull the rock or plug and take it to "the lab". I have a 4 watt laser that I use to burn them off. If for some reason I can't get them with the laser I'll just glue over the spot it's growing from. Once I've finished attacking them the rock goes back in. The next day I repeat the process again. I've been doing this for a month now. The first 2 weeks I killed aiptasia almost everyday. Now it's about once every 3 to 4 days and I'm only finding one here and there. I don't know how aiptasia works, but I want to say that some spores remain dormant until things are "ok" before they sprout up which is why I am still finding them here and there.
I've had to do this process before on my zoes that I put into my frag tank. That was pretty straightforward though as there were only so many places they could hide on a frag plug. Rocks are more difficult as they have, depending on the size, multiple places to hide.
It's a lot of work and it's not over yet but I know it's working when I only see one every couple of days. Before it was 5 everyday.