Ruger No. 1 in .300 Win-mag is available with a .26 inch barrel - fits the criteria you mention below, but the price tag is a bit high. IMO if you want to reliably take elk at 500 yards, you'll want a bit more energy than the 1,000 ft.-lb minimum conventional wisdom and some state's hunting regulations dictate. While some .30-06 loads @ 180 grains plus achieve 1,200 ft-lb at that distance, .300 Win-mag can easily get you over the 1,500 ft-lb mark. Actually the single shot concept makes good sense at this distance.
Good point, oof another caliber to stock, and reload.