At only 500yds, any of those calibers will do just fine (as will your current rifle).
The 7Rum will have less recoil and shoot a little flatter, with a fast twist and heavy bullets, it's a nice cartridge.
The 300Rum is a serious hammer that will last a bit longer than the 7RUM and is plenty flat shooting out to 1000yds.
The 338RUM can be jarring in a light rifle
, In a heavy sit and wait rifle, it's not bad.