I think that this'd be cool too... I think that the timeline for GSG9's should just be slightly different... The Battle of Britain is won by the Germans as you said, but they manage to pull off a successful invasion in Operation Sea Lion and they set up a fascist state in England.
Much of the British Navy, including one aircraft carrier, is turned over to the Germans, but others escape, refusing to take orders from the Germans.
Great Britain itself has been knocked out of the war, but the rest of the British territories are determined to fight on and liberate the homeland.
Without the Great Aircraft Carrier of Britain, the Americans have no way to get over to Europe except through Africa... but Rommel manages to secure northern Africa by early 1942, and so that means of entry is cut off. They'll have to fight northward from Nigeria, but that will take years. Meanwhile, the Americans do much better against the Japanese in the Pacific Theater.
But disaster strikes... unmolested by Allied bombing raids and having handily defeated the Russians on the Eastern Front, Germany has had plenty of time to develop it's super weapons. Amerika Bombers begin raining destruction on New York, Washington, and Boston by the spring of 1946. Then a German ramjet bomber flying at suborbital altitude drops a dirty bomb on the city of St. Louis deep within the American heartland. With that, the U.S. government sues for peace and is forced not only to make peace with Germany but also to make peace with Japan in spite of all of the gains made in the Pacific.
1947...
In the wake of the devestation, the world is being reorganized along new and terrifying lines. Germany has been forced to make peace with the Communists of Russia, but it is very likely that soon fighting with recommence... since Soviet partisans continue to wreak havoc in German-occupied Russia and eastern Europe. India has been lost to the Japanese as well as all of Southeast Asia and northern Australia. Fighting continues, however, but without support, they will not hold out for long. Resistance in India, Southeast Asia, China, and Australia is fierce... the Japanese are losing a lot of men and also inflicting horrific casualties on the locals.
In Brazil, the fascist Integralists threaten to take control of the government thereby starting a domino effect within Latin America. Getulio Vargas must not fall if South America is to be held by the Allies. In South Africa, the Afrikaners under Oswald Pirow rebel against the British control in South Africa. They have 150,000 soldiers and even more members of their movement.
The Americans meanwhile are biding their time. They will not let the slaughter of thousands of innocent Americans go unpunished. They are rapidly developing nuclear weapons... but within the country, there is a rising voice crying that the destruction has been a lesson... a lesson that America must join with the fascists, that if it had not been for the "socialist" leader Roosevelt, America would not have had this terribly tragedy befall it. The country is on the verge of being torn in two.
I think Canada ought to be grouped with the Free British.
There should be a separate Afrikaner group.
There maybe even ought to be Fascist Americans and Integralists sprinkled throughout their territories...
Also, there should be paramilitary forces throughout German and Japanese-controlled territories.