You are looking at the options available to Hitler from a retrospective post war view; i.e already assuming that WW2 would be a war of attrition. From Hitlers point of view being conciliatory and magnanimous to the western democracies was pointless (see his attitude to British Empire and how little dividend it paid him).
In December 41, he was pretty much master of Europe, despite setbacks in the Russian hinterland, it was reasonable and not insane for Hitler to assume that the Russian Campaign would be wrapped up in 42.
If that had happened, and Germany been free to direct its resources west/mediterranian again, there was nothing what so ever to fear from America.
Declaring War on the US did not change his position in Europe much, it would be years till US could make its presence felt in Europe; it would help him in two ways though. Intensify the blockade of UK (which did happen and was again a close run thing) and give Japan a tremendous boost.
And Hitler was right about the impact of making war on US, very little of consequence happened till the middle of 44, by which time his goose was cooked anyways on the Eastern Front (see Bagration) which for Germany in World War 2 was always the field of decision.
Hitlers declaration of war on the US might have been a debatable trade off, it was hardly an insane one.
Regarding Japan, it was a case of devil and the deep blue sea. An oil embargo pretty much forced their hand. It was either cave in and give up the empire or fight for it and sue for peace from an advantageous position.
Regarding negotiated peace, world war 2 was pretty much an anomoly in that the Allies refused to negotiate and demanded unconditional surrender. The norm before before ww2 had always been of wars being concluded with a peace treaty.