I have been an avid backpacker, hunter, and fisherman for the last 45 years. Joined this site because it has been a goal of mine to hike the AT during this entire time. My sons were raised backpacking, hunting, and fishing in the Black Hills of South Dakota/Wyoming, the Big Horns of Wyoming, Yellowstone NP, Glacier NP, and the Rockies of Colorado. The Rockies are well documented on the CT, but if you want to avoid crowds, you might want to consider the Black Hills or Big Horns.
Resupply is very limited if none existent. Posted trails are limited. Some of both areas require bushwhacking. You are totally on your own if an injury occurs. Fishing is great in both locals. I would be happy to provide inside information to anyone that wants to PM me.