Actually that's pretty much following OTL, Garand was still in .276 at the time. The one difference is the Pedersen is not off gallivanting in Britain, as by lucky coincidence the Greeks adopted 7x51 some years before (just as in OTL they decided to standardize on 7mm in 1924 and the two available options were Pedersen's 7x51 and 7x57 Mauser, 7x51 fitted better to what they had in hand.) and thanks to the Zaharof/Vickers connection Vickers picked up a licence for his rifle early. The interesting question is whether Pedersen's presence manages to get Douglas McArthur to chose .276 over 30-06. After all there is the little fact that the existing 30-06 could not be used with Garand which needed different ammunition and Pedersen is the right man to note and point out this...
True, I had forgotten that a .276 version of the Garand had been created for this trial, but this is after the 1924, 26, 27, and 28 trials which had it be chambered for 30-06, and it was Garand's work on the .276 prototype that was then also scaled up to (30-06 developed in parallel in case something like what in otl happened, happened which Pederson hadn't) that helped him win over the Pederson rifle due to greater simplicity (less points of failure and reduced chance for problems developing) and reduced cost.
Honestly, its really the cost that I believe will still sink the .276 cartridge as, re-looking at my sources, even though .276 Garand came inches from being adopted as both army and cavalry loved it due to reduced weight and recoil with no loss in military effectiveness. After all, It was cost in otl that caused McArthur to reject the round as the both the BAR and machine guns the army used all used 30-06 and either introducing a second ammo type to logistics or redesigning those guns to fit the new round would require money the army just doesn't have at the time.
Of course, with Pederson in the states he may have been able to compete with Garand longer and potentially talk down McArthur's ultimate veto of his cartridge, you are the author after all and unlikelier things in arms procurement have happened. But with the US Army, cost is the ultimate bugbear that I'm not sure can be gotten over. Either way, the .276 Garand is an interesting thought and could be one of those fun differences with the timeline.