I don't care if you're hunting squirrels or the biggest Grizz in the region with a sheep fitting somewhere in the middle, I'd go with a 300 to 338 mag shooting high BC bullets.
My thoughts are regardless of the animal you're after you need to a big heavy bullet for 600 yards and battle the wind. Add to that, something that's a deterrent to bears takes you to 30 cal and above. Sure, a 6.5 creed would do the job but you're approaching the limits of that round and don't even get me started on the 6mm's. Again, I feel like most people don't consider the wind when these type situations are brought up.
This is a very expensive hunt and possibly once in a life time. As stated above, if that critter walks out on the last day you don't want to be horse power limited. You said build not will dads trusty ole aught-6 work...If you're building, then no need to marginalize things.
I wouldn't hesitate to roll out with my 9 pound loaded 30 Nosler. I'd consider trading in my 230 Bergers for some 200 Bull Dozers or Hammers but I'd be ready to sling led or copper to 800 yards.
One last thought FWIW and purely my personal opinion. I've only been on a few guided hunts. While it's there job to keep me safe, I ultimately take full responsibility for my own safety. My guide had some suggestions on shedding weight on a NM Wilderness hunt this past fall. Most of it was around safety and water. I took his advice and removed some but not all.
