Dan, there isn't a need to regulate positions at this time.
If you look through the player cards, you'll see that the type of players in this league play multiple positions (they needed to so they didn't get shipped back to the minors!).
So, there is sure to a big excess at all the positions, except possibly catcher and starting pitching; and in those positions there will be enough, but perhaps not a big excess.
Depending on the results of the nominating stage, we might need to put a cap on the number of catchers you can draft, but the rules already specify there will be at least 2 C for each team.
Plus we are all drafting one superstar pitcher, and, with the possible exception of Tatum, they will all be starters. That leaves only 4 starters to draft and if you look at pitchers in the salary levels of 1.0 mil and above, the starters are clearly worse than the relievers. So, plenty of bad starters will be nominated and be available for the draft.