It appears that with Play All, I could effectively do this an unlimited number of times, moving all the Creepers in the game to wherever I wanted them. Is this correct?

A: This is an unfortunate loophole with the card as written in the first several printings. It was intended that you could only use it once per turn to move a single Creeper. We updated this wording as of approximately September 2016 (but there are a lot of decks out there with it open-ended like this). If you’ve been playing it over-powered like this, you’d be within your rights, since it does not technically say “once per turn”. Now that you know the intended usage, you could still choose to use it as written, however, we’d prefer that it be nerfed as follows:

Our official ruling would be to play it as if it said “…once during your turn you may move any Creeper from one player to another, then put this card back in your hand.” Of course, if there were a multiple play situation, you might subsequently play it again to the table, but would not then be able to use it to move a Creeper again on your turn.

As always, “once per turn” means once per YOUR turn, not once on every person’s turn.
See For special Keeper (or Item) powers or Rules that say “once per turn”, does that mean…