This new 6.8 seems like it is more in line with 280 British
And, that's probably a good, modern, comparison. The .280enfield (very briefly the .280nato) was like 7x52.
Historically, we have the .280ross and the .276pedersen and the .276enfield which are 7s with case lengths from 52 to 56mm. Their differences were typically in bullet weight and BC. They generally were all pretty high chamber pressure cartridges (which is why the P-1913 was such a heavy design, it was meant for the .276enfield).
So, this is not "undiscovered country." These trails have been traveled before.
In US service, the .276pedersen could have been a spiffy rifle cartridge, but, it was not going to be a very good MG cartridge, and the M2 Ball could be stretched out to 3200m in a 1917 or 1919--and the training and doctrine of the day mandated needing those sorts of fires. That was 1934-5.
In the 50s, the Brits rolled out the EM-1 and EM-2 in .280enfield, and that was looking like a great alternative to the militarized .308 and 7.62CETME which were competing for acceptance. The .280nato just could never be "good enough" for MG use out to the desired 2000-2500m ranges UK wanted. And, their budget did not allow for two kinds of ammo. So, the bent the knee to the 7.62nato. (Which the US did not get into general European service until 1962, to start dumping it in 1966-7 for 5.56nato.)
The Brits even tried out a 4.8mm replacement for 7.62nato before 5.56 was adopted. Chinese PLA also fielded a 4.8 briefly with their ugly bullpup (they kept the 7.62x39 for their RPD variant).
What was old will be new again.