I've also got a sudden urge to make a map based on what you described.
Do it! that'd be something to see.
Heck, i could see this being a full-on TL-191 AU setting. Call it "Southern Victory: Invicta Britannica" and have the main protagonists be the new generation of CSA rulers who are starting to wonder if they backed the right horse in GWII.
To add to my concept, and bring up Russia and Italy, Japan, following Russia's economic collapse at the end of the Second Great War, purchased Russia's East coast, particularly Vladivostok and a large portion of Siberia, as well as, by default, securing control over Manchuria and Korea and exerting influence over Mongolia, losses Russia readily accepted as the badly-needed influx of cash allowed the Provisional Government to regain control of "European Russia" amid a series of strikes and riots in her major cities following a major famine in Ukraine, where German-loyalist bandits from the time of the German occupation deliberately sabotaged crops with bioweapons provided by German scientists.
Flush with resources cleaved from their occupations, particularly the discovery of Oil in Manchuria and the mineral riches of Siberia, Japan stands as the unquestioned master of Asia, with territory and vassal states stretching from Siberia to Australia. Pundits on both sides already foresee a "War of Emperors" as Britain and Japan square off over India and the UK's other holdings in Asia and the Pacific.
Italy, meanwhile, has thrown its lot in with the Neo-HRE in a desperate bid to stave off being gobbled up themselves, as the Racial and Religious Extremism of the British leaves the primarily catholic nation with no doubt as to their fate in British Hands. Spain and Portugal likewise join the HRE, the latter invoking a ruthless multi-superbombing of Lisbon for their "Betrayal" of their centuries-old Alliance with Britain. Spain, for its part, sees initial successes, and Gibraltar falls to the HRE after a long and fierce ground and naval battle.
Under the leadership of Kaiser/Holy Roman Emperor Louis-Ferdinand I, who took the throne after the assassination of his brother Wilhelm IV, who himself had to take power after the sudden death of Wilhelm III in 1951, The Neo-Holy Roman Empire was formed as much out of expediency as desperation, and indeed the French King in exile, Charles XII, "rules" from the German city of Bonn, as virtually all of France has fallen to the British Imperium, as has Belgium and the Netherlands. German capital helped keep Austria-Hungary from imploding at the cost of Austria swearing fealty to the Hohenzollern throne, finally achieving, in a bleakly ironic manner, Frederick the Great's desire for Prussia to become the dominant Germanic state and hold the Hapsburgs as vassals.
This internal success does little to change the shape of the war, however: While a mass-superbombing of the sort that annihilated Lisbon is impossible thanks to Germany's own atomic weapons (thus inviting annihilation in kind on Britain should Germany be so attacked) the Sheer Numerical and Material strength offered to the Imperium via her reclaimed colonies and the sheer amount of men and resources coming from Canada and British America has forced the NHRE firmly onto the defensive. Overtures to Russia to lend her manpower to tilt the balance in the NHRE's favor have fallen on deaf ears, as the Kerensky government can barely hold on to power as it is, let along drag Russia into yet ANOTHER war.
British Imperium and Vassal States:
United Kingdom home Islands, including the whole of Ireland.
France up to the borders of the regions of Hauts-De-France, France Est and Bourgogne-Franch-Comte. (these three regions are legally recognized as "France" by the NHRE)
Corsica
Egypt
Palestine
Madagascar
All British, French and Belgian Colonies in Africa
Canada, including the dissolved Republic of Quebec.
US states North of the Mason-Dixon line, including Illinois, Michigan, Iowa, Wisconsin, Pennsylvania, the New England States, Indiana, Ohio, New York, Nebraska, Idaho, Delaware, New Jersey, Montana, Minnesota, Dakota, Oregon and Washington State (incorporated into British Columbia)
(Utah is legally recognized as Deseret, and is basically Neutral ground)
Bahamas
Bermuda
India, Pakistan, Bangladesh, and Burma are British-held territories, as are Australia and New Zealand. New Guinea is contested between the Imperium and the NHRE.
Allied States:
Confederate States of America
Second Mexican Empire
Republic of Columbia
Republic of Nicaragua
Republic of Honduras
Republic of El Salvador
Republic of Costa Rica
Republic of Belize
Republic of Guatamala
Kingdom of Peru
Republic of Argentina
Kingdom of Bolivia
Kingdom of Paraguay
Kingdom of Uraguay
Republic of Ecuador
Republic of Venezuela
Republic of Guyana
Kingdom of Suriname
French Guiana (Occupied)
Neo-Holy Roman Empire
German Empire and her territories (German West Africa has fallen to the British, but she still holds East Africa and her Pacific holdings)
Austro-Hungarian Empire
Kingdom of Greece
French Empire (including Algeria)
Kingdom of Poland
Allied states
Ottoman Empire (Turkey, Iran, Iraq, Syria, Jordan, Saudi Arabia, Afghanistan, Turkmenistan, Armenia)
Kingdom of Sweden
Republics of Finland, Lithuania, Estonia and Latvia
United Kingdoms of Norway and Denmark
Kingdom of Italy (including Tunisia and Libya)
Republic of Spain (including Spanish Morocco)
Republic of Chile
Kingdom of Brazil
Republic of China (mostly nominal, as they have their hands full fighting the Japanese)
United States of America Government in Exile (Several thousand Yankees who fled to Germany with the bulk of the US Navy after the end of GW2)
Republic of Libera (Liberia, Guinea, Ghana, Ivory Coast, Togo, Benin, Burkina and Sierra Leone, Major Democratic state, Conquered by African Americans who fled ahead of the CSA victory in GW2. Largest Naval power in West Africa)
Kingdom of Ethiopia
Japanese Empire
Japanese home islands
Korea
China as far inland as cities of Wuhan and Kunming
Tibet
Nepal
Manchuria
Russia/Siberia as far west as Lake Baikal and as far north as the Arctic Circle
Indochina/Vietnam, Laos, Cambodia
Thailand
Solomon islands
Philippine islands
Taiwan
Malaya
Indonesia
Just to help lay out the map