So I finally got around to giving the Sanitaire a little test run a few minutes ago with its new bag system in place. It worked fine the way I put the bag in—snorkel first—so I guess that's okay. Overall, I'm very pleased with the setup. It's the way the machine should have been all along.
I cannot attest to the exact fiber content but to the touch, the new the outer bag feels like the same cotton canvas as the original bag; in fact, other than having a zipper up the back, you'd never know it wasn't the original. I'm guessing it may be new old stock.
I finally gave up on trying to pull the metal header off the dump bag and just put it down in the barn, dirt and all. I even tried standing on the bag and pulling it with both hands. It just wouldn't budge, which further reinforces that buying the F&G kit was the right call.