Only "Full Proof" way of eradicating with possibility of saying "I am free" is to completely remove all acros from the tank and hold in quarantine. In order to do so, you would need to have another tank setup that could house these acros. The most successful way of removal would be to cut at each of their bases, this would isolate the coral only for dipping and removal. The acro bases in the tank would need to be destroyed, therefore no living acropora tissue in the tank. I would recommend 90 days, IMO their is no certainty to egg lifespan, however, I am confident that this would be generously enough time in quarantine. Before the corals go into quarantine, they would need to be dipped, having plenty of fresh saltwater in buckets would be advised. Once in quarantine, observation and regular dipping is advised. After 90 days, dip all the acros before making their way back into the display. The tricky part is, that this is a heck of a lot of change, which acros are sensitive to, so there could be collateral damage along the way. This is why I prefer to by fresh cut frags, they are easier to dip and tend to not have the flatworms, even if the tank the frags are coming from have them. There is however no guarantee.
Or you can simply live with these worms and have predatory type fish that eat them, acropora crabs which usually don't allow for them, and simply baste as you see the corals releasing film when all others are not. It is like the slime that comes off them when they feed, or have been taken out of the water, then put back in. Basically a defense system to protect themselves, however, if they are releasing it, when all others are not, then something is irritating it. These are the corals I would baste. If you excessively baste a given spot, over, and over, yes you might upset it, possibly damage the tissue. I assure you however, this is not going to kill it, as in the wild, waves crash on them, they are even exposed during low tide, baking in the sun for hours, until the tide comes up again. You can do the basting method and have beautiful glowing corals, in fact the healthier the coral is, the less they seem bothered by the little buggers. Don't be under any false belief that AEFW don't get blown off with powerheads and displaced in other areas of the tank, like on the liverock, sandbed, glass, overflow, etc... I discovered I had them by seeing one on the glass of my tank during dark hours, not by finding them on a coral. So again, there is not a guarantee unless you quarantine, or live with them. Sorry for the lengthy reply, but wanted to weigh in on my experience. Best of luck, keep updating the thread to share with us what you do, and how your experience goes...
Regards,