20 of the 28 franchises have been taken twice in each of the league's three seasons, so one idea would be to broaden the range for the remaining franchises to make them more enticing. Those not taken the maximum six times are:
5: Florida/Tampa
4: Cincinnati, Chi. Cubs
3: Baltimore, Anaheim, Texas
2: Chi. White Sox
0: Detroit Tigers
Maybe make these teams 1960-69, and after this season other ideas could be explored for adding some variety?