Indeed. I think the conservative nature of Army procurement might still see .30-06 prevail, but I would vote for the .276. It actually makes the BAR more sensible, full-auto-ish, Mg-ish, potent round, the partner to this new "lightweight". It lets the Army dither on about replacing the M1919 with a true GPMG the infantry can carry. As wiking points out, the .276 Garand might sideline the M1 Carbine, thus the Army has .45 M1911/Thompson, .276 Rifle/Carbine, and .30-06 BAR/MG. Not logistically far from OTL. I will not predict a SAW at this point but things like the Johnson LMG might get a better look at, the .276 might spur development of a better BAR weapon for the Squad. Of course that seems to suggest the 6mm arguments here argue for .276, rather than a new round as such. Would the USMC persist with the 1903? It occurs to me they might not prefer this new rifle or its round.
Not the .276 Garand, just a .243 Garand. The 7mm Pedersen was too powerful to make it an M1 Carbine replacement, the 6mm version would be light enough to do both roles though.
A .276 Garand would not have sidelined the M1 Carbine as there was still a requirement for a light handy weapon to equip truck drivers, mortarmen, radio operators etc. The US army was not happy with 1911's or Thompsons in that role as they didn't have the required range or accuracy and even a Garand in .276 is too big and heavy for that so something like a M1 carbine is always going to pop up sooner or later given the way the US military was thinking.
I suppose if they adopt either the .276 Garand or keep the .30 version then they might opt for a SCHV Carbine assuming that they still heed the report from OP. Then we might see a .20 caliber M1 Carbine, later on in the war with select fire and a 30 round magazine. That would be a true assault rifle.
In fact something very similar to what a .20 caliber + .351 WSL rimless case cartridge would be exists now:
https://en.wikipedia.org/wiki/.20_VarTarg
Granted though it's performance relies on high energy modern powders to get to 1000mps at the muzzle, so not necessarily practical in WW2 from that sized case and uses a 24 inch barrel, but it shows what could be possible. By all accounts even the most powerful .20 caliber cartridges with 1200mps muzzle velocity are very low recoil and aren't hard on the barrel of a rifle, so would make for a very controllable automatic weapon cartridge.
As for .276 stimulating a true LMG/GPMG in US service, you would first need to bang a lot of heads together in the Pentagon and Springfield, the US seems to have ignored the introduction of the ZB26/30/Bren family and the MG34 along with the tactical flexibility they offered. The M1919 was a good weapon (for a vehicle) or in a MMG role and the BAR was a weapon, sadly they were both deficient when it came to modern warfare.
Not even just that, but the FN BAR modifications:
https://en.wikipedia.org/wiki/M1918_Browning_Automatic_Rifle#Belgium
QC barrel, simplified construction and takedown, and better rate reduction mechanism. That's not even counting the belt feed options a few people developed for the weapon. Forget the competition to the BAR even, just the modernization efforts for the BAR could have made it a cheaper, easier to make weapon, that worked better than the base version. Really kind of odd considering even the Soviets were able to develop a swap-able belt feed mechanism for the DP-28.
Maybe the USN and USMC never ditch the Lee round.
That would be the easiest option in the long run, but difficult to pull off in the short run.
I'd suggest have the French adopt their 6mm cartridge/SLRs that came out of their modernization project, but that was arguably only ready years after the LN was dropped.
Plus the 6mm LN cartridge had issues beyond that which would be worked out with improvements in powder and barrel metallurgy:
https://en.wikipedia.org/wiki/6mm_Lee_Navy
Finally, due in part to its long, thick-gauged semi-rimless rim case and beveled rim, the 6mm Lee was one of the most expensive service cartridges to produce in terms of cost per round, yet it was already becoming obsolescent in comparison to ammunition that used more efficient powders and true rimless cases.
[9] Rapid developments in military small arms ammunition would soon demonstrate the advantages of a magazine-fed rifle and machine gun cartridge with a rimless case and spitzer bullet, features not found in either the .30 Army or the 6mm Lee.
[26]
It was of course adaptable, but that would mean significantly changing the case production lines anyway.