Are you talking a new barrel? If so, time to ditch the belt, though the problems with a belted magnum are over rated. Assuming you reload. I'd step up to a .284" bullet if Elk are in the mix.
A 28 Nosler would be sweet as a hunting gun that does not see a lot of rounds down the barrel. 7mm PRC Is perhaps a little kinder to the barrel if you shoot more. For that matter, lots of decent 7mm RM brass out there too, if you want to ditch Wby brass and keep the belt - 7RM does not seem to burn up barrels as fast as the real overbore 7s. You could probably build any number cool wildcats on that action too.
Whatever you do, think it through and research. Decide your personal maximum range I think first. Consider the bullet class you desire thereafter (weight, SD, etc) and then work forward. If its 400 yards, life it easier. You can choose a medium weight bullet and aim for some speed. You want 1000 yards? You are in the swamp. Judging from the 163 posts since 2009, Indypendent is not a sudden 1200 yard shooter, but that's just me making inferences.....
Lastly, should you be partial to the .277 bore, there are lots of manufacturers making tighter twist .277 barrels capable of running the heavier .277 bullets. A 270 WSM, 27 Nosler, or keeping the 270 WBy are reasonable options with a new barrel with an 8 twist or so. But personally, I think elk with a .277 is something left to skilled experienced shooters. If you are in that category, don't need a guide telling you what to do etc, then OK....