I got two elk in the northern NM mountains last year, and I can only echo the need for a sturdy bullet. My cow took a (too fragile) 7 mm round and made about 400 yards till she finally stayed down. For the bull I used a 308 168 gr TTSX, it made it through the elk lengthwise intact.
I used to love being able to hit hard at 1000 yards. As I get older I find hitting a mini ram at 200 yards with the 22 oddly more satisfying.