If you guys are considering DW, there's another PbtA game called Night Witches that is AMAZING (and I don't use all caps lightly) and specifically had rotating GM as part of the game play. It's not a Groundhog Day situation, so it it probably isn't what you want, by its worth checking out.
The game centers around the lives of female Russian bomber pilots in WWII. It rotates between a night cycle where bombing missions (pretty lethal ones, to reflect history, but there's also the a bevy of characters to be cycled in) are carried out; and a day cycle, to deal with the relationships formed in the crucible of an incredibly misogynistic Red Army that literally set these women up for failure. The author, Jason Morningstar, had done several interviews about it, but there's a good episode of a podcast called
+1 Forward where he explains the inception of the project and does a little demo playthrough with the host.
Like I said, probably not what you want, but it's so worth looking at just for its own sake as well as seeing how it implements rotating GMs.