Do you have any frag putty/aquarium putty? If you made kind of a tower/extension so that the birdsnest was at least an inch away from the rock, if not more, you could put it on that. Then the birdsnest would get decently big before it spread down to where the zoas were. A decent-sized birdsnest frag on a zoa rock would probably do okay fending the zoas off, so it could be worth a try.
Alternately, you could put it in one of those bare areas, and put a ring of frag putty around it. Then, whenever zoas grow onto that ring, just cut them free of the colony, remove the ring, and put a new ring.