It might be possible to kill them all eventually, but it would probably be quicker and easier just to dry the rock out if you can (depends on fish and coral load).
This might sound a little crazy, but if you can't afford to leave the rock out for any kind of extended period of time, I'd try a blow torch to literally torch them off (I'm thinking a nice air/gas mix with a really blue flame could scorch them off fast enough without literally cooking the rock and killing everything inside of them). If you want a cheap torch with a really nice blue flame, pick yourself up a creme brulee set... and then you can make a bomb diggity dessert too.
It'll probably kill a lot of your coralline, but that'll happen if you dry them too. Just do a few rocks at a time so you don't flood the tank with too much dead stuff and invest in a group of peppermint shrimp (find big ones if you can). Copperbands can help, but they'll eat worms like crazy too and might bother some LPS.
Some people have said peppermint shrimp don't work, but I swear by them, and obviously bigger ones will eat more. The issue is, with a problem of your scale, the aiptasia can reproduce faster than peppermints could possible eat them... so you'll never get ahead of them. That's why I always add pepps as a safety measure to prevent a problem, rather than as a solution to an already existing problem.
I've never had a tank yet that didn't have at least a couple aiptasia somewhere no matter how hard I've tried (and anytime you add a coral you risk carrying in a little one), so I don't think the goal should be total elimination, but rather control.