I say allow existing GMs run the open teams, requiring the second team be in teh other league. Thsi is done in several leagues i am in. I have seen GMs switch to the second team. The only caveat i woudl throw out is not allowing 1st round draft picks to be traded away as this will cause new GMs to leave (when tehy cant draft).
I would be willing ot run a National League team, if needed.