I can live with that, to be sure. I think I just need to replace one player to make it work cleanly. The point is that each player should only count toward one position, whichever that is. I think we could even submit our rosters with that designated, so I'd have to declare that Player C was on there as a SS, for instance.
The more I think about this league, the more I think the rosters should stay hidden until after we draft. If we all have to evaluate 24 (or 16?) rosters and figure out how to rank them, that's going to take a big chunk of time. Realistically, you'd need to input all of them and analyze them for strengths and weaknesses, because you can't tell anything from a list of names and seasons.
I'd even be fine with just a random assignment of teams. You get what you get and make the best of it. I'm not sure a draft is really needed.