Good reply GE. I however always had the impression that the RAF was nearing collapse due to exhaustion and over demand on the existing pilots and that the only thing that saved them was the sudden transfer to daytime bombing of London rather than the strategic bombing and attacking of airfields.
The other notion of Luftwaffe cooperation with the Kriegsmarine is one of those factors that has everything to do with Goering and Hitler's attitudes and medieval high court nature.
Goering adamantly opposed offering any of his own planes to help the Kriegsmarine and when he finally was forced to make a minor concession to his sea going 'brethren' he offered only obsolete planes in marginal numbers which were still under command of the Luftwaffe and not the Kriegsmarine. This led to the U-boats never receiving proper air support in eliminating targets or in searching them out. At this point Hitler's favour was a thing that went deeper than strategic importance or even competence. They vied for it like hungry savages and Goering's arrogance caused the evisceration of the Luftwaffe in seeking their primary celebration as the sole capturers of Britain's surrender. This appealed to a Hitler not wanting to face a seaborne invasion. Also to consider is that since favour fell to the Nazi elite, the Kriegsmarine received little heed when challenged by Hitler's old standbys since it was the least 'Nazi' member of the armed forces of the Third Reich. Though in later years, as the other cardinal members of Hitler's inner circle failed him, and even Doenitz became a primary figure and remarkably at the end of the war the actual commander in chief once Hitler died, for too long the Kriegsmarine was not given its fair share.
So to consider the notion of cooperation 'twixt the Luftwaffe and Kriegsmarine in a proper sense is to consider a different leadership of the Nazi party altogether.
And I think killing Churchill would be an interesting outcome, but not very fun for a game since immediate surrender without an invasion isn't that fun is it? They gotta at last fight for the beaches a little bit.