markg262, look at the Theme League Classifieds and the Progressive Leagues.
In particular, jimcraven74's theme league called "no cookies" MLB107623 (use the "edit league option" at the top of your team's draft center page and then click "existing theme league" and put that number including the MLB prefix with no spaces in between) allows only owners with 5 championships or fewer and does not allow certain "cookie" players that are overused in Open Leagues that are part of the strategy of veteran champion owners.
There are two spaces left in that league now, so you might be able to get a team in now.