The exorbitant cost factor for DH's needs to be kept under control for this to not only work in both leagues but retain some level of parity between bigger and smaller markets.
These guys don't play the field and all. Literally never pick up a baseball and shouldn't command huge salaries that are out of context with the rest of the players. The players union can throw up a challenge, but it really is the rank and file members of the same union who are hurt by excess money going to part timers. Then you could get several good DH's on a team.
How about two or three of them, to hit for you suckiest hitters at your discretion?