Back when I had only one key, I made the muling game with the receiving char --- that way I had to leave the game and come back with the giving char after the 5 minute wait, which basically "proved" that the game was still there.
It's a bit of a tradeoff, though --- that "first char change" counts towards your realm down. Just be patient --- you can alway Alt-Tab out of the game and do something else for a bit, like checking the forums. And mule *often*, instead of muling a lot of stuff in one session.
EDIT: and don't go overboard: don't mule the 5 SOJs you got in the last 5 games in just one session. Move them one-by-one.