The line problem may have it's solution in the same way you receive delicious meats and cheeses.
How about, at get-togethers, challengers make one big line and take a number. When a leader is free they call the next number on the list. When your done fighting, you go to the end of the line and get a new number. If you have the badge of the leader who calls your number, switch numbers with the person behind you until called by a leader you haven't fought yet. This way everyone gets a turn.
The numbers could be printed on Avery Business Cards or could even be scraps of paper handed out by a bored E4 or Champion. You could even get a white board with "Now Fighting #" on it. It'll be like a Poke-deli!