As of now, they technically negotiate separate from the rest of the league.
As you can see on this page (scroll down to "Production Rulebook", there are separate ones for the Broadway League and Disney. I haven't gone through them side by side to tell you if there are any differences though.
Yes, I know they negotiate separately. I just don't know if Schumacher joining the League as chairman will affect that. I don't know much about how the League runs.