Average mule deer hunting? Definitely an adjustable peep sight with a medium or small hole. I bet it wouldn’t be hard to hit a 10” target at 300 yards with a little practice. I had a peep sight on a Remington 700 with a very large aperture and I want to say off the bench we could get 2 or 2-1/2moa groups out of it on a good day with a big black square on a big white background and we held at the bottom of the square, but the younger the eyes the better. It seemed we could hit paper better than a 10” plate - at 300 yards the plate was pretty safe, but we didn’t put much effort into it and the ghosts ring rear sight wasn’t ment for long range.
Some long range shooters add a “bloop tube” to the end of the barrel to increase sight radius - it’s just a hollow tube fit over the factory barrel and extending 10” or so. I don’t recall exact group sizes, but the best target shooters seem to get groups around moa.
Oh, it just hit me - search for long range muzzle loading hunting - those guys seem to have some good setups.