Gas operated rotating bolt assault rifle (6.5mmx50.5mm rounds).
It says
here that, from 1932, Swiss company Oerlikon owned the foreign/international rights to the design. So the US/UK could manufacture under license. SI victims take note!
They already had a gas operated, rotating bolt rifle design...the Garand and M1 Carbine. Which were turned into the AK-47 by the Soviets, who liberally borrowed from those designs.
I doubt the US Army will accept a 6 mm or smaller cartridge before WW2. The Navy had experienced issues with bore wear and possible failures to stop Philippine fighters with the 6 mm Lee. The early high velocity cartridges of the day were still novel experiments. The Army was conservative. It was considering smaller caliber cartridges. Early experiments favored 6.35(.25) to 7(.28) caliber cartridges. The .276 Pedersen or a rimless 6.5 Arisaka would have been perfect.
The Scotti open bolt would not be acceptable for the US Army marksmanship requirement. The heavy thump during firing would reduce target shooting scores.
The Lee Navy was harmed by the shitty metallurgy of the day, which meant the barrels weren't up to modern powders. Not an issue by the 1920s.
Plus the reports about stopping power in the Philippines weren't corroborated, in fact the fighting in Cuba showed very different results.
You're right that the caliber studies looked into 6.5mm-7mm as the ideal (the Kent Report from the OP took those results even further), but the conservatives went as big bore as they could and settled on 7mm; the .276 Pedersen was far from perfect, but it was the best that could be gotten through the infantry board at the time. The Arisaka is better, but still not really ideal.
The Scotti was meant as an anti-aircraft gun for defense against low flying aircraft, so of course it was meant to work as an automatic, but that wasn't hard to change if desired.
When the Swedes adopted their 6.5mm Swedish Mausers, they eventually decided to chamber their machine guns in 8mm Patron m/32, which was basically 8mm-06 with a wider case (170 gr at 2,800 fps) to fit in Browning actions. Any cartridge smaller than 7 x 57 Mauser would probably require this kind of split with pre-1930 propellants.
They only adopted the 8mm for their heavy machine guns because they were meant to be an anti-material/anti-aircraft weapon and very long range. So they wouldn't even take the 8mm Mauser and instead mated the Mauser caliber to the American .30-06 cartridge case to push the 8mm bullet to the max as well as be able to use the heaviest bullet possible. In a sense it was their 9mm MAS/.338 LWMMG.
Frankly the other Europeans and Americans should have accepted that the ideal solution for an MMG/HMG and an infantry rifle/LMG would be so different that it would require different cartridges. Give it to the Swedes for being ahead of the game.
The original caliber testing, started by the Army in 1925, found that an oversized .25 was the most effective of all, over the .276 and .30, for the report of the "Pig Board" tests in 1929
It had a 125 grain bullet@2659fps with a 55.9mm long case.
Indeed, which I think led to the Kent Report in OP about small caliber high velocity rounds being the most lethal.
BTW where did you find info about the case length and muzzle velocity? I've been trying to find info about the Pig and later Goat Boards and can't find the reports.