I knew of the .276 Pederson being tested by the US, but thats first I've heard of their testing the .276 British. Makes sense though, since if adopted the rifles and ammo may have been produced here just as the P-14 was.
Cordite was no good for the .276 British and if it had been mass produced they would likely have developed a Pyro-Cellulose loading for it.
The P-17 like the 1903 was a adaptation of the mauser design. The lee Enfield is a updated and improved American design to begin with.
Theres actually next to nothing about the P-14 thats distinctively Enfield, aside from the shape of the grip. The rifle was a complete departure from previous British designs.
Also there are a few mutts out there, P-14 receivers fitted with M1917 bolts and re-bored to 8mm.