In order to shift the Alliances, and to keep Germany (and Eastern Europe) out of the communist hands, the new German government would need time.
I, and nobody will never know, if without the Western Allies push and the Strategic Bombing the Russians would have been able to win.
I tend to say yes, but…

How much time the German Government would need to negotiate, not only a separate peace but also a change in alliance?
I base the idea of a successful killing on the 20th of July.
So, what decision to take?
In term of military you can’t just withdraw all the troops inside Germany then deployed them just in front of the Russian without a Western Allies guaranty they won’t take advantage of this to invade the national territory…
You can try to negotiate a separate peace with France, Belgium, Holland and all the others governments in exiles, but how much chances you have too persuade the French Army which is soon to land in Provence to stop here and not pursuit…
The massacres of Oradour sur Glane and Tulles by the 2nd SS are from June. It would be difficult to the new German Government to convince the new French Government (as by now Petain’s Government is completely discredited) not only to cease-fire but to help against the Russian, which they help in their war thanks to the Groupe de Chasse 3 (Fighter Squadron) Normandy, at this date Normandy-Niemen (21st of July 1944) and Soviet Union Hero (Gold Star of Hero of the Soviet Union, Red Star Order, Red Flag Order and Lenin Order, plus some others)…

I agree with PJ, the biggest mistakes would be avoid, however I am not sure it would avoid the Eastern defeat…

“The loss of either of those would not have collapsed the German economy. Normal exchange rates could have been sustained in the short and medium terms without much impact, and women were a vast untapped resource throughout the war.”
On other matters, the release of the prisoners and the immediate cut in raw material, which would need to be compensate, would create a vacuum that Germany can’t easily fill.
To replace the Slave labour by the German Women labour would need more than just a shift in personnel. Most of the war factories were linked with the Labours Camps, and the logistic chains adapted (and work conditions) to the first kind of labour.
I spoke with one French Woman (refugee from Croatia in Serbia as she was married with a Yugoslav she met during the WW2 in Germany) who was in Forced Labour.
She worked for Siemens and all the work force was specialised and couldn’t protest against working conditions.
It wouldn’t be easy for a new Government to let these people to go (and de facto to provide the means of transportation) and to create more suitable premises for the German Labour to take their places… It would need time.
Would Germany have the skilled man/woman power to produce the ME 262 without the Slave Labour? I doubt.
It would need time to reshuffle the war industry, and this even if the Western Allies agree with the plan…
Time it wouldn’t have.

Because the Western Allies can decide to use the moment to push their advantage.
And the Russian as well.
Would the SS fight to hard in the boccage if Hitler would be dead?
Even the regular Heer would be in disarray…
How to avoid what happen to the Menshevik in 1917 when the Russian soldiers decided they had enough and “voted with their feet”…
Some the best German Generals were Nazi as e.g. Model. Kesselring and Sepp Dietrich for the best known. Would these Generals gave-up and agree to this, especially after an assassination and Coup?