Just throwing this out there, but would the ARRL, (or any other governing body for that matter), have any jurisdiction or authority on the moon?

The answer is yes, but not the way you are asking it.

The question is not whether they have jurisdiction over the lunar territory. It's whether they have jurisdiction over their own awards (DXCC, VUCC, etc) and contests (Field Day, etc). And the answer to that is clearly yes.

Steve W3HF