I didn't read the whole thread.
But I would split the rock into sections. Throw the first section into the tank your going to treat. Feed all the aiptasia's so they are big and fat, and start injecting them with kalk. Granted this will mess up your water quality and calcium and ph will be all over, but that it why you dont do this in your actual display tank. Kill as many as you can with kalk, and then send them to another tank full of peppermints and bergs. Let them take care of all that's left over. When that's done, move the rock into the display.
start over. also keep peppermints in the display to eat the little ones that will almost certainly be left behind. Be sparing with the kalk, as if you inject too much and it drips out, it will kill all coralline it touches.