My Son and I have hunted for years with rifles chambered in both .270 Winchester and the 6.5-284. They're great choices and you can't go wrong either way. You started off saying you were looking for a cartridge that's "wildly available" and of course if you want a factory-ammo cartridge you can get in any backwoods hardware store the .270 is it and the 6.5-284 isn't. If you roll your own . . . we've had wonderful results with both.
While we've never had noticeable trouble with the Norma cartridge feeding, as some report with its rebated rim, I feel the time-proven .270 feeds smoother and magazines will sometimes hold an extra shell with it. If I was re-barreling, and I actually do have a similar project in mind soon, I'd stick with the .270 and just install a 1:8 or 1:8.5 twist to take advantage of the newer high-BC bullets available.
In our limited experiences, with Elk and big Mule Deer, the old standby .270 Winchester just lets the air out of their sails a bit quicker. I can't say why that's so, as it sure doesn't look any better on paper. My Grandfather hunted with the grand old cartridge so, to me, there's also a sentimental aspect involved.
Whatever way you go, happy hunting Sir!
SF -