Not sure that is entirely accurate. Morgenthau, Eleanor, and his daughter had much more of a role in the last 12 months of FDR's life than Marshall and the rest of the cabinet. If you want sources for that I have several books on the internal politics of the administration. The media also covered for him heavily as well.It might have worked.
Hitler was swimming in a witches brew but FDR was submerged in a cauldron of his own, desperately ill and tapping on death's door on a plethora of highly experimental drugs for diabetes and poliomyelitis while slipping quite badly mentally. He was mostly lucid but he suffered frequent diabetic comas and periods of confusion. Sometimes he could be out of it for days, clearly unfit to serve. He was protected and the problem concealed from Congress and Vice President Truman by Chief of Staff George Marshall and his palace guard. They were running policy with Churchill around FDR and saw no reason to follow the law and turn over National Command Authority, maybe mess the grand plan up, as there were many with actual authority that had great reservations. This was much the same as a similar group did at a crucial phase of the aftermath of WW1 for Wilson, after his stroke if that's really what it was, a move that probably lead the world directly to WW2.
If the Germans had pulled off a last ditch operation Martin that could possibly extend the war in Europe to 1946, FDR would have been forced by political necessity to come out of his cocoon of protection and show himself in order to hold his party. If he had slipped, had a spell and Congress or Truman suspected how soft in the head he was getting, FDR would have been set aside as unfit and Harry S. Truman would have become acting president.
This could definitely have caused a policy change. Truman, a WW1 combat veteran that had been there and done that and got elected by veterans hated the idea of throwing men away. He had no love at all for the Soviets or their pawns infiltrating the west, a problem of which he was well aware. He had not been briefed on anything that wasn't in the newspapers by Marshall's Palace Guard and walked into the job absolutely cold in OTL, inheriting a policy and team that barely deigned to talk to him at all or do anything but present him with papers to sign for one fait accompli after another, a group that he couldn't rid himself of in victory.
George Marshall was also quite old, ill and within a few years of death, possibly losing the thread himself given his later failures in China and being propped up by his own staff. He was, according to Dean Atchenson, 'under performing like a four engine bomber on one engine.'
FDR, Marshall and Co. never had a problem showing their disdain for non-aristocrat outsider Truman, who with his Confederate roots had never been rich, had ties with the Pendergast Machine and had actually worked for a living. Truman got to his position by chance, hard work and with the support of the veterans of his old US Volunteer artillery unit, a politically powerful group in Missouri that held their former elected commander in very high regard.
The old-money group that had accreted itself around FDR would have been placed directly under Truman's thumb at a time when Truman could easily have chisled them free, replaced them and changed US policy.
Marshall was if anything more a figurehead for the public by the end of the war than a political powerbroker as far as I can tell.
Given how sick FDR was I wonder if the shock of the defeat would actually speed up his OTL fatal stroke in April 1945. BTW Stalin himself suffered a stroke in May 1945 and a major heart attack in late 1945 as a result of heavy smoking and drinking (much like FDR and Churchill). Since Truman was way in over his head when he first got in office I do wonder if it would be too much to cope with if FDR dies in say January or February in the aftermath of the biggest military defeat in US history (it would be equivalent to Stalingrad from August 1942 to the surrender of the pocket in terms of casualties just in the German offensive period, not counting the Aachen-Hurtgen fighting).
As to FDR-Truman, that was probably more a function of the party bosses forcing FDR to dump Wallace as his VP in 1944 rather than any particular problem FDR had with Truman. FDR wanted his guy, but wasn't able to fight the way he could before by 1944, so that probably colored relations (or the lack thereof since they only met once privately before FDR's death) much more than anything. As to Truman he was more independent than you think after WW2; he did after all fire Morgenthau, Roosevelt's buddy with an iron grip on Treasury, in June 1945 over demands that Morgenthau was making on Truman's administration (he apparently thought he could bully Truman and found out the Missourian was no pushover).
Though I do agree with you that Truman taking office earlier after a discredited FDR either dies or is pushed aside would have much more freedom to do as he pleased to clean up the mess.