ORIGINAL: Fan Club
I'm sure it could be adapted, you would either have to install a row of snaps on your vest or switch to something like a velcro system. Either way it needs to be adjustable.
The problem I see is how to attain just the strap. They're only available with the Hunter Specialties S.U.V. (Sport Utility Vest) that I'm aware of. H.S doesn't market them as a separate accessory.
Now that you have the idea, I'm sure you could fabricate one. Be sure it has a rubberized inside surface to grip your gun stock.
First of all, I'm a novice (n00b) turkey hunter as last year was my first season. So, apologies to Fan Club for a rookie chiming in to agree, but I like the "gun buddy." I bought an Ol Tom strap vest last year and it has pretty much the same stock strap, and I happened to use the HS Strut knee rest and thought the whole gig was mobile and comfortable.
My dad and a brother have Primos Gobbler vests (they've hunted turkeys for a few years) and they liked the gun buddy thing, so I modified their vests to make them. Hammered a black link of small chain near flat and sewed it into the shoulder, then cut the nylon strap and plastic clip off an old suitcase or gym bag and sewed the loop. Worked like a charm. My dad is 76 yrs old, so the strap, a Lazy Leg gun rest and a comfortable seat help him sit longer.