If you aren't wedded to wrap, you can use a clear recycling trash bag. Slide the tray inside, let some air in the bag, twist it closed and voila. You have protected the dough from air currents, and the bag is lifted away from your dough. It may take a bit of technique to remove the tray without having the bag deflate and stick, depending on just how sticky your dough has become. But a brief contact is much less of a problem then having your dough grow into the wrap.