I've thought of a way to get this going with less participants...
Instead of doing random teams, we could do random divisions and use offensive and pitching awards to determine the winners.
This is what it'd look like.
Let's say I randomly get AL East. If the HR leader, or Cy Young, or Mvp, pitcher with the most saves or k's etc comes from my division I would win for that specific award.
Since there are 6 people interested, that'd be easy... there are 6 division. We'd all just need to agree on the sts/awards we'd want to use to determine the winners.