The anti-Hitler resistance might then get the assurances from the West about Germany getting a negotiated peace if they topple Hitler and overthrow the Nazis, which could well trigger a successful coup.
If Hitler gets that lucky and, for the POD to work, he does not botch Operation Blue, there won't be a coup. He'd be seen as a god and military genius.
Unlike some, I do not find a negotiated peace impossible in this situation as you lay out. Vichy France was already considering more active support of the Axis, offer them their old colonies in the Middle East in exchange for the use of air bases in Algeria. It makes Britain wonder why keep fighting, they just keep losing.
As for the Russians, the Lend Lease will be starting to come in, but without any victories on land and any hope of the Wallies opening a real second front for at least a year, they might sue for a temporary peace.
However, Hitler probably is an arrogant nut and thinks he can have total victory. So this means he needs to get to Baku by 1943 to get his oil. By then, he kept the war going too long which means the Wallied strategic bombing campaign is starting to have an effect and the Torch landings will go down. The war then will go long enough to let Germany be A-Bombed.
Really, Germany's only hope is Britain goes:
Honestly, with the Blitz in the past, I do not see any chance of this, even if Churchill is ousted. The Nazis have lost all credibility when it comes to peace. As long as the US is in the war, Britain will fight. And I don't see the US dropping out even after all these defeats...they would look like weaklings. So the US continues, and that means Britain continues. And Russia will continue as long as they can by default because Hitler won't let there be a peace.
So, Axis still loses...hard.