I think Murphy knew he couldn't hold back Wolf and Gutey forever. I think he was able to convince TT that by giving up the GM job he could spend his time on the part of the job he likes best - Scouting.
I don't think there was any convincing going on. Ted was ready to step out of the limelight.
If anything, the move likely precipitated Wolf's exit from the front office.
When the going gets weird, the weird turn pro ~Hunter S.