With the prospect of an "honourable" peace with conditions could the war have been over by late 1944? In Europe and the Pacific?
There would be no "honorable peace." Any backdoor negotiations with the Allies would result in terms that would make it apparent that unconditional surrender from Germany was what was demanded.
People make too big a deal about the negative impacts of FDR's declaration in my opinion.
Most of the Axis did negotiate their surrenders. In 1945, the Allies did have backdoor negotiations with Japan; Truman specified Japan's unconditional military surrender to indicate retention fo the Emperor would be acceptable; and Japan did try to use the Soviet Union as an intermediary to negotiate a peace.
Certainly, the politicians and military in Germany and Japan used it for some propaganda value, but the declaration also benefitted the Allies.
1) It made sure that Stalin knew that the US and UK would not accept any separate peace from Germany.
2) It pacified a public deeply upset about the negotiations with Admiral Darlan during Operation Torch.
3) It let the rest of the world know that the Allies considered the unconditional defeat of the Axis to be inevitable at that point.
4) It ensured that the defeat of the Axis would be by military means, ensuring forever that no one could ever argue the frontline troops had been "betrayed". After the war, no German or Japanese could argue they could have won or kept their conquests. For long term considerations of peace, this is fairly important.