“Anybody know why they were considering .276 caliber?”
I don’t have a definitive answer, but it appears that after The Great War there was a line of thought among the various War Departments that a .30 caliber cartridge was more powerful than necessary for most purposes, and a .276 cartridge was adequate and, being lighter, lessened the load carried by an infantryman.
There was at the time, and still is btw, a school of thought that the .27 caliber is about the ideal for combat purposes.
Hence the drive to 'upsize' the 5.56 to 6.5 mm (.255 caliber).
The British before WWI had decided to go to the 7mm and developed a new rifle, the pattern 14 Enfield for it. Their decision might have been greatly influenced by the fact that the South African Boers used the 7mm Mauser with great effect against them around the turn of the century.
When WWI began, the decision was made to stick with the .303 to prevent supply problems. I think I have read that Churchill himself made the decision.
The pattern 14 was chambered for .303 and contracts made to have it built in America. When the U.S. got involved in the war, we could not provide enough 03 Springfields and the decision was made to modify the Enfield for the 30-06, thus the 1917 Enfield.
...from Wikipedia:
"At the time of its introduction, the .276 Pedersen was a solution to a significant problem. The US Army wanted a general issue autoloading rifle that would fire the .30-06 cartridge, but such a rifle was prohibitively large with existing designs such as the Browning Automatic Rifle and French Chauchat. A weapon of the same weight as the M1903 needed to fire a smaller cartridge. Pedersen's cartridge was viewed as a compromise as it was underpowered compared to most military rifle cartridges. This decreased recoil energy made possible a reliable, lightweight semi-automatic rifle with existing technology. Despite these early problems with semi-automatic designs, Garand's design was eventually able to handle the .30-06 cartridge; the need for a lighter caliber dissolved. The Pedersen rifle was unsuitable for the .30-06 and it, too, was dropped."
See my previous posts above. The real irony is that the great bulk of WWI production .30 caliber ball had unannealled case necks, and by WWII case neck fractures were frequent enough that most of the older *war reserve* ammo was unusable in the automatic actions of .30 Brownings, BARs- and M1 Garands. A good deal of it was burned up in training, though, and served for stateside guard purposes.