Here is a suggestion:
Minimum number of seasons played (in all leagues): 5
Plus: Minimum winning percentage (in all leagues): 60%
Plus: At least 4 playoff appearances (in all leagues)
Or: At least 3 division championships (in all leagues)
Or: At least 2 conference championships (in all leagues)
Or: At least 1 league championship (in all leagues)
The key is minimum number of seasons played and all-time winning percentage. I am unsure as to the number of GMs that would be eligible under this criteria, but I don't think the requirements are too onerous. In fact, they might be too lax. I would be interested to hear others' suggestions as well.
It would also be interesting to require GMs who don't succeed in the "big league" to step down and allow other successful GMs to enter the league. Perhaps measured by having a winning percentage of less than "X", e.g. 45%, over a five season span. It would make it much less likely that a GM would tank to get a better draft choice unless he figured that there would be an immediate turnaround.