Maybe I am not much help - I am like the various posters above who tend to want the gun in hand when going "out" and maybe expecting or hoping to use it - but I do like having a carry strap in my pocket to install for the "trudge" back to the truck.
In the past, I have owned a side-by-side 12 gauge and a side-by-side 45-70. Both were made by Baikal - so neither would be considered "high end", at all. But they both had capacity for sling swivel attachment ahead of the forearm - was a small base with a swivel stud - was drilled and tapped into the rib that was between those barrels - two screws - has been a while - my recollection is "small screws", but no longer sure if that was #4, #6 or #8 - most likely some metric size within that range?
That leaves the butt end - to install a stud or not - my current side by side - is 20 gauge - I use a strap - just a loop on one end to slip over the pistol grip, then "tie strings" to go around the barrel - and I do tend to carry it barrel pointed down - as shown in that movie picture above. I have also seen leather "butt pockets / cuffs" that lash over the butt plate - I think made for lever action rifles - those "pockets" usually have a stud on their bottom or perhaps user can attach his sling swivel to the lacing - allows the use of a carry strap without having to permanently install a stud on underside of the butt stock - I never used them, but likely best idea for barrel pointed "up" type of carry strap carrying?