As an update, my filefish have now eliminated most of the aiptasia on the ~15-25 lbs of rocks I put in there, which were pretty infested. I've started feeding them a little more but they also are continuing to slowly eat the remaining aiptasia. At this point the population of aiptasia is small enough that they'd have no chance to reproduce faster than they'd get eaten, which is good.
It seems based on which aiptasias are left in my tub, the filefish greatly prefer eating small ones rather than big ones. This is different from my experience with the nudibranchs who seemed to eat big or small ones with no preference. I noticed this eating preference among my filefish because the first aiptasias which disappeared in the tub were the tiny little spawn that had attached to the sides. Then this preference became very apparent because at this point the only ones left are big ones, everything small to medium size has been eaten.
So perhaps a good strategy is to kill the biggest ones with a syringe and not worry about the little spawns that activity will produce because the filefish will take care of those quickly. At least that is what I'm going to try when I import the next batch of rocks. Also to re-iterate what I said before, the filefish are not particularly voracious eaters of aiptasia. Killing the largest aiptasias manually would not be wasted effort based on what I'm seeing. But if the filefish will eat all the new spawns quickly then they are still doing a very valuable service.