I think your final para is right...a compromise climbdown... no losers (except Shoigu's face maybe).Here Prighozhin goes further than he ever has gone before.
He does not intend to give up his army, that much is clear. But it's hard to see what his strategy is. His men, as far as we can tell, are loyal to him. But he's totally reliant on Russia for supplies and money. If he refuses to hand over his men and they refuse to sign by next week, we reach an incredible impasse.
The golden case scenario is that he decides to turn his forces around and march to Moscow, Putin is then forced to pull back from Ukraine to defend, then those two are left to bumfight in western Russia. It seems highly improbable that he could convince his men to do this, but could it be that's what the videos are about? To prepare the ground for such a move?
If he loses his army, he not only loses all power, but is likely to be killed very soon.
The important thing to remember, is that whatever is going to happen will happen next week. The Kremlin will surely turn off the taps of money and equipment if Wagner don't comply and it's now or never for Prig.
To be clear, my money is on a Kremlin climbdown and Wagner to continue as normal. But that outside chance of civil war is keeping me very interested in developments.