It woudn't matter that Goering was incompetent, Hitler was no model of competence either. What would matter is that the invasion of SU was tripped up at a crucial time, and didn't go ahead. This would ensure Germany remained a self-reliant superpower rivalling the SU and USA. Over the winter months of 1941-2 a proper leadership team could emerge, which could be satisifed with the gains up to April '41 plus whatever was taken from the Brits afterward.
That's the whole idea about Göring being a "better leader". Nazis relied on the "Führerprinzip", thus an almighty leader decided all. Göring is weak and incompetent, and happy when just representing the ideology and getting cheered. Thus who rules the Reich during warfare?
1. Himmler has no idea about military and strategy and was also laughed at by the other Nazis
2. Goebbels has no idea about military and strategy, but is maybe the most fanatic one. Thus he'd want to ensure the Reich to live on, but he wouldn't be that involved in military decisions.
3. Borman: I don't know about his military skills. I think Borman would be the strong Nazi, the one that rules with Göring celebrating himself. But would he lead the warfare? No.
4. The Gnerals would do the main job. I think ITTL, with Hitler dead, the Generals would increase power, such as during WWI with a weak Kaiser unable to follow their ideas and oppose their plans. Additionally, Borman would rule the party and the state and support the Generals in a symbiotic relationship of winning the war and surviving Nazism. Goebbels would be the voice of this group, Himmler would sooner or later loose his power, since the Generals wouldn't accept a Waffen-SS, neither would they accept ressources taken away from the fighting troops to support the SS-agenda.