I have watched this thread with interest and some amusement, but I do believe such a premise could be interesting. I think I would stick with one position (PG, SG, SF, PF or C) of a team's choosing, and let as many teams as they like choose that position. Recruiting will still not be cut and dried, as teams would still have to find guys within that position to fill certain roles (a good BH center, a good REB PG).
I wouldn't necessarily force a team into a particular game play, as it forces the coach to devise a game plan for for his team's (and his opponent's) very odd strengths and weaknesses/ Decisions like playing an all-center team fast-paced against an all-PG team to maximize possessions could work or backfire. What is the best offense/defense for an all-center team to play? The possibilities are wide open.
Alternatively you could allow only recruiting from one state, or only players whose last name begins with the same letter. In this scenario, everyone has simply handicapped their team with poor players, and the team that wins could very well be the team that gets lucky in recruiting (for their letter or state) a couple of seasons in a row.
While I think playing against one another in conference will be loads of fun, the real challenge will be if you can create a team that can compete in the NT. In that case, a team made of all one position might indeed have a shot.