Maybe there is something inherent to the .300 RUM that make very narrow SD's of velocity impossible. Try all the usual match case prep stuff along with neck sizing and see if that doesn't shrink the spread. Also try a Federal 215M primer, if not already.

I've never owned a .300 Weatherby, so I don't have a good first hand feel for its SD potential - but wouldn't be surprised if it was in the same boat as you describe with the .300 RUM. The few I have built over the years can hit a pie plate at 500 yards reliably, but not much better than that. Both are great hunting rounds, though, at least for 99% of the hunters out there. The situations where the rifle, shooter; and conditions that could come together to make a 500 plus yard big game shot a responsible venture are pretty uncommon. Yet its nice to know you could, at least on paper . . . . . Roscoe