If I had the funds available to go on a truely "
once in a lifetime" hunt it wouldn't be in the states. Hunting moose or elk or caribou really isn't that unobtainable for the average person if they really want to go. Make yourself put away 20 or 30 bucks a week and you can literally go every five to six years on an Alaskan hunt.
My list of once in a lifetime animals would include.............
Asia for Marco Polo sheep and Ibex.
New Zeland for trophy red stag.
Africa for Gemsbuck, Kudu, Eland, Sable, Zebra, and Cape Buffalo
Marco Polo Sheep

Ibex
.