It'll be key to watch how Republicans in the legislature behave. They could try to remove the Governor from the redistricting process, but voters will have to approve it. What I will say is that if they wanted to do that, it basically costs nothing. But the big failure of the North Carolina GOP's amendment schemes this cycle might help instill a sense of futility in the WIGOP. Although walking away from this election with little-to-no erosion in their legislative ranks might embolden them. I dunno.
Also there is no guarantee the WIGOP has a state Supreme Court majority by the time the maps need to be redrawn. I think Democrats have some opportunities, and at worst, the GOP will only have a small majority on the bench.
Edit: Actually, seems like Republicans will likely have a bare majority for redistricting, but that hardly means the GOP will just gerrymander through them instead, if it falls to the judges.
Couple things: 1) There is not enough time for Repubilcans to get a Consitutional Amendment on the ballot in time before 2021. It has to pass in two consecutive terms. That is unless they call a special session before January. 2) If there is a deadlock regarding redistricting, the federal courts will get the authority to drawn the lines, not the state courts. Look at Virgina for example.
Are you forgetting who controls the federal courts?
It would be a random district court judge chosen from the Western District of Wisconsin (because it covers Madison). All three currently active judges on the Western District of Wisconsin were appointed by Democrats (two Obama, one Carter).