I think the criteria ( of mine) works for hunting these steep mountains. The rifle is carried and seldom shot. I won't carry my 25/06 any longer because of the long ( 24") barrel.
I am a .270 wcf user but it easily is bull elk capable with the new, effective bullets these days. I think the .243 will be effective also with a ttsx or Swift bullet, as long as it creates a deep wound channel it will work.
A Barnes ttsx, Cutting Edge mth , Hornady GMX are nearly unstoppable.
Things have changed quite alot.
I hunt elk every year and have killed bulls at my own place on occassion but I like to hunt the high elevations and I gotta carry the thing on my shoulder to do it. The lighter, shorter and compact the better for me.Cheers