I've got a rifle with the 58 cal barrel tapered to 15/16" at the muzzle. But it's 1 1/8" at the breech. I'm betting that the loss of 15/16" 58 cal barrels from the market was due to lawyering and the concern for potential bursts from overloads. Right up there with McDonalds coffee in the lap. Even so, I bet you'll have trouble finding anyone that will build a 58 x 15/16" barrel, much less do the rebore of a smaller cal. I guess if I needed to worry about it I'd be looking at the rear sight dovetail and how thin the metal would be, then locate the rear sight as far forward as you're comfy with.
BTW- On the question of hogging out the stock to make more room for the barrel, my rifle evidently started life as a 15/16" TC Hawken. Lots of hogging going on back there to make room for that 1 1/8" breech end, but whoever did the work managed to pull it off. The wood is real skinny in a couple of spots around the lock plate, and I probably wouldn't have bought the gun in the first place if I had popped the barrel beforehand. (Note to self.) But it seems to hold up fine, even if it's a little scarry lookin down there.
Another BTW- For whatever reason, the smith opted to use a 1" tang (fixed) rather than a 1 1/8", so there's a definite step betwee the breech and tang. Makes me speculate that the smith wanted to keep a little more wood in the tang than would have been possible with the next size larger.
Hope my observations and speculations of an existing conversion help.