I came up with a rig for my LTD as a one point sling. I do not know how those AR fellas keep the strap on their body...but I came up w/a set up that I use hogging in the marsh hammocks. I have a velcro strap around the grip(yea it's not great..) and a single attach point to it...over my shoulder and clipped to my jeans(now to a double strap suspender(and I look goofy in suspenders))
It carries the gun high and I can keep a bent wrist over the top of the stock. I do this on the LTD and my .44 both having straight stocks. I get max flexibility which I need as were I hog you go from 0-100 in 2 seconds and I have complete freedom to swing and rest.
Tree stands and the like I remove any strap.
You should google the Youtube vid of fast shooting a 45/70 for a bear charge. It shows how fast a lever can be brought to... bear.