Jim; You posted the following;
"If I were to start such a round robin, it would bounce back and forth in and out of the U.S. on each step of the journey."

If I understand your post correctly, that would mean you would need the same number of non-U.S. room key participants for each U.S. room key collector, otherwise some participants will be paying for U.S. domestic priority delivery while others will be paying the more expensive International postage fees depending upon where they stand on the routing list.