Thanks, that's very helpful. Everything checks your list except maybe the embossed edges; they just look like plain ol' edges, to me.
The family rifles were the Winchester M71, a Savage M99, an early (as far as I know, especially given the likely age of the scope) Winchester M70 Featherwight in .270 Win, and a Remington 760 (I think) pump in .30-'06.
The other sling also fits the Savage studs. Both the M71 and M99 studs are wider in diameter than most modern pieces, so the jaws of the swivels need to be wider too... and they are, in both of these slings. I don't have last two in that list, but maybe I could guess that maybe the other sling might have originally come from the M70 FW instead of the Savage? Given the Winchester-like characteristics (keeper staples, frog-hooks, swivels)? I can't think why the other sling would belong to the Remington.
-Chris