Please don't dismiss a double as way outside your budget. While it takes some hunting, you can find great calibers, like 450-400 3 or 3&1/4, or 9.3x74 (which is ballistically just below the .375 and still legal for buffalo in SA and elsewhere) for prices in the 5-7,000 range.

If you go with a bolt and really want open sights, you should also consider a peep sight which, particularly for gentlemen of a certain age, will be quicker on target and more accurate than express sights, because you are only looking to place the front sight on target rather than lining up the v and the bead correctly with express sights.