Get rid of the draft and go with a free-for-all with spending limits. The initial limits are based on a weighted ranking of team records over the past four years (35-30-20-15)
On Opening Day (the end of the offseason), rank all 30 teams in terms of free agent dollars guaranteed. Then, dock the highest-spending team 15% of their amateur pool, the next highest 14%, and so on until 15 teams have been affected.
There you go. No player or team is treated unfairly.