Let me know what you finally settle on Rich. I'm tempted for a .308 cartridge along the same lines as you're thinking. One very experienced member on this Forum has convinced me that the 300 RUM yields a fairly short barrel life. His POI's and MVs kept changing because the bore was eroding so quickly. He shoots a lot more than I, but if a guy's gonna shoot very much, the 300 RUM seems like too much case capacity. Too much overbore. The 338's seem to shine with that much case capacity.
Can't believe I just typed that, now that I admit that I own a .257 RUM. But I don't shoot the .257 RUM very much at all. Got it more for the novelty item that it is, than anything else.