They must be asking the appeals court not to do anything about appointing a new judge till they hear back from the SC about the appeal at that level. If they can get the court to agree to that and then think up 3 or 4 reasons to appeal to the SC, they could hang the process right where it is for a few weeks.
I don't know if the court will be inclined to go along or not. I don't know of any reason the appeals court can't select a judge and let him begin reading the previous material before the SC rules on the appeal.
Jay