I would consider the 270 WSM,the 270 Wby,
the 7 mag, 7 WSM,and even the old 264 WM.

The 270 has excellent heavier bullets with decent BC's(150gr@.525BC) to fly further predictably.

You may also wish to get an optilogic range finder to compensate for the up/down shooting angles and get the actual horizontal distance to shoot encountered in the mountains.

Sounds like fun!!