There has been no response from what I can find from any Michigan GOP official or Trump campaign lawyer.
I’m surprised that in the 10 hours since this ruling came out we have nothing.
Trumps legal team has been lackluster at best. Like you said there is no excuse for them to not already filed briefs with the 6th circuit and let folks know they are seeking immediate relief. If Trump gets somehow denied Presidency or this goes to the House, his incompetent legal team will be to blame.