I think you’re asking a lot of the right questions: how to add more variety, how to make the game more truly global in scope, how to create advantages for the Allies without overcorrecting. I’m not sure how well you’ve thought through some of the specific changes that you’re recommending.
Moving the British ships from Gibraltar to east Africa does nice things for a British naval presence in the Indian Ocean, but it makes it way too easy for Germany to win the Battle of the Atlantic – Germany can now routinely take out all of Britain’s ships in the Atlantic on the first turn without taking too many risks. This means that Germany can totally evacuate France on turn 1 and probably also on turn 2, which gives Germany a big advantage against Russia.
The Sea Lion threat is probably exaggerated – sure, if you spend 100% of your economy on ships and planes for India, then London could be in trouble, but it’s pretty easy to build, say, 4 infantry in London and still have enough cash left over to place a variety of units in India. Britain starts with 43 IPCs, and London’s not that hard to garrison.
Meanwhile, Japan’s ability to take India or use it as a base to threaten Russia is almost entirely gone. One of the key threats the Japanese have in OOB Anniversary 1941 is building a factory in Indochina on turn 1, capturing Burma turn 1, and then threatening to build a factory in Burma on turn 2. If Japan pulls this off, then it doesn’t matter if Britain has a factory in India, because Japan is still outproducing Britain 4:3, and Japan will wind up with all 3 factories, which can then churn out infantry and tanks to head for Stalingrad. On the other hand, the only way Britain can prevent Japan from pulling this off is by sacrificing its entire starting force of troops from India and Persia, which is expensive and leaves Egypt vulnerable to the Italians.
In your version, Burma is only worth 1 IPC, so there’s very little point in having Japan build a factory there. Japan can’t take Bengal until at least turn 2, and the UK starts with a factory in India, so even if Japan gets a factory in Indochina right away and an eventual factory in Bengal, that’s very unlikely to be enough to deal with the forces Britain will have been accumulating in India proper. The Indian factory is almost 100% safe against anything short of a massive naval invasion – but that naval invasion is much harder to pull off assuming even a modest USA presence in the Pacific, because Britain now has two extra warships in the Indian Ocean, plus a starting factory there.
I think the dance of attacks and counter-attacks you outline in West Africa is entertaining, but unrealistic in terms of strategy – if you’re playing to win, then nobody cares enough about French West Africa to bother sending a transport there. Allied transports are much better off going to Morocco or Gibraltar, and Axis transports are much better off going to Gibraltar or Egypt.
Finally, I don’t think an Indian factory is likely to have any effect on the war on China – it’s 3 moves away from the nearest Chinese territory, and likely 4 or even 5 moves away from the Chinese front lines by the time forces actually arrive.
What all of these admittedly nitpicky corrections add up to is a sense that your changes won’t actually deliver that much variety. You get a different scenario with your changes, but it will always be the same different scenario: Germany wipes out the British Atlantic fleet and then charges hard for Moscow while Britain easily holds London and India and stalemates Japan. The USA can choose to either knock out a weakened Tokyo (and try to get to Tokyo before Germany gets to Moscow) or rush toward Paris and Rome (to try to set up a stable beachhead on the Western Front before Germany gets to Moscow). Other than the USA’s single choice of whether to go to the Atlantic or the Pacific, nobody has any interesting grand strategy decisions to make. Italy has to fight for Egypt, Germany has to fight for Moscow, Russia has to fight for Moscow, Japan has to fight just to hold onto a decent income, and Britain has to defend London, Egypt, and India. The details will vary from game to game based on tactics and dice, but I predict you’ll see a lot of the same general campaigns over and over again.
You may be interested in this earlier thread about splitting India and splitting the Indian Ocean:
https://www.axisandallies.org/forums/index.php?topic=41826.0