RBernie said it best if assuming what the OP listed was the range, which--right or wrong--I was as well:
"6.8SPC, assuming that the definition of 'intermediate' implies an OAL that is less than 2.26" (or 57mm). It has the broadest performance envelope and product availability of any AR friendly chambering."
But LK makes some very good points if you loosen the criteria out to a broader context, which also makes sense. Make mine 7mm-08 of the traditional short-actions or .308 family--does most of what the .308 does, flatter and with a bit less sturm und drang, making it just about an ideal "battle rifle" round I'd think (real world ramp-up/logistics aside)--in addition to being a time-proven "all round" hunter (mostly medium game). I wouldn't usually consider a .270 Win an "intermediate" round in today's context" (thinking stereotypically AR platform as that)--unless we're hunting Africa or Alaska--so I wouldn't consider 7mm-08 such either necessarily...as it's effectively a ".270 lite," only bowing to the great Win in 300+ shots. Thus, my original 6.8 response like RBernie's. Within the OP's list/context, to me the 6.8 is similarly a "7mm-08 lite"--being optimally limited to ranges under the -08's effective reach. And, even if one is talking AR platform (and no one says that, but...assuming), I'd agree that, in terms of caliber/cartridge, "intermediate" starts at 6mm, but still limited in OAL.
For us old timers out there, I also liked the .30-30 comments someone made. Have shot that great under-rated round for years. Obviously limited--at least til Hornady/Leverlution--by action type, a few bolts out there notwithstanding, still a great classic/traditional intermediate do-all if loaded and bullet'd up right.Yes, I know a x39 is "essentially" a spitzered .30-30, but IMO it still is a lesser round without quite the punch within their respective effective ranges if that makes any sense!