What about simply having the 30-06 accepted at end of WWI by Britain and France, say US offers them a deal where by they get the large number (2M ish) of M1917 Enfields surplus in return for spending the development money on paying off more of the US war debts?
All three then have the same small arms cartridge and simply develop a belt fed BAR as the light MG in 20s and a joint semi auto project in 30s? With an emergency MAS36 also being built when its realised that France cant wait for the ITTL Grand/MAS39 trials to finish......
This is the perfect answer if the future was known - however that's a catch 22 isn't it? If the future was known it would be different! They had just fought the war to end all wars and I don't think that rearming for the next one was hot on their list of pretty much anything
So Britain and France don't need 2 million rifles - they have an extensive war industry configured for their own needs and millions of their own rifles.
The British have a good rifle in the SMLE, over a million P14s (a .303 version of what the US turned into the M1917 built in the same factories). A very good LMG (best in class) in the Lewis and a very good MMG (best in class) in the Vickers.
The French are in a similar position and both have millions and millions of rounds in their respective calibres.
As for the M1 garand production never really caught up with demand until 1943 with some fighting units (such as 'Chemical Mortar' companies) going ashore at Torch armed with Springfields.
The Marines at Guadalcanal and the soldiers fighting in the Philippines were not issued with M1s and I have seen pictures of some soldiers as late as 1945 in Europe still armed with Springfields.
Indeed if it hadn't been for the M1 Carbine being such a good weapon that it was used in the front lines - there would very likely have been 'non-riflemen' members of fighting companies, engineers and artillery still armed with the Springfield and likely the Eddystones
So M1 production struggled to arm the US Army until mid/late war let alone anyone else until then.
Just want to say at this juncture that I think the M1917 Eddystone was one of the finest bolt actions of the period - really confused why the US kept the much older Springfield design over it?