You should check out Gun Werks out of Montana who runs 7mm mag, 300 mag, and the ultra versions of those rounds as well and take down brown bear, elk, and moose out to 1,000 yards repeatedly.
Also Christensen Arms out of Utah, they make a carbon fiber barrel for their guns for stability in varying temperatures, and typically run a 300 ultra out to 1,000 yards.
I think you'll find that for that size game the real question is what BC does your bullet have, cause to be honest a 308, 30-06, 7mm mag, 300 mag will do just fine at that distance as long as you use bullets like the heavy grain Berger VLD bullets that have outstanding ballistic coefficients.
Just my .02