I don't see Goering being any more willing to avoid antagonizing the US then Hitler did. Like the rest of the German leadership, Goering believed that conflict with the US was inevitable from lend-lease on and it was just a matter of "when". He also shared much of the leaderships contempt for American war making capacity, as revealed by his remark to Rommel that claimed the American's made good refigerators, but not good combat aircraft. There's also the fact that Goering's position within the Reich is far less secure then Hitler's. He doesn't have the loyalty from the bulk of the military and Nazi Party apparatus that Hitler did. Him refraining from antagonizing the US and trying to abandon the, by this point, quite old relationship ("alliance" is rather too strong a word) with Japan is just going to further destabilize his already precarious support base.
This probably comes down to a Anglo-American vs German-Japanese war, with the Soviets watching gleefully from the sidelines. Japan is likely defeated as per OTL, but whether Germany is defeated depends on the political will of the Anglo-Americans hold up to prospect of paying the blood price necessary to defeat the German army which is something of an unknown.
This probably comes down to a Anglo-American vs German-Japanese war, with the Soviets watching gleefully from the sidelines. Japan is likely defeated as per OTL, but whether Germany is defeated depends on the political will of the Anglo-Americans hold up to prospect of paying the blood price necessary to defeat the German army which is something of an unknown.