Recoil is very subjective and is more dependent on stock fit than caliber. As an example I had a post64 M70 that weighed about 9 1/4 lbs in -06 that kicked a lot off the bench. Had a M700 in -06 built with a custom fitted stock that came in at 7lbs. With the same load the M700 was perfectly comfortable off the bench. Also since you are talking about a hunting rifle how many times in a year are you going to shoot off the bench? Is recoil really going to be that big a deal?
As far as calibers go just about anything will fit your criteria although since your western trips are quite a hike from TN using something that would allow less than ideal target presentation may be a consideration so something between 257 and 284 seems like it would do the trick.
Hmmm I think I just recommended a Kimber in 270.
You have a lot of options.

Last edited by Blacktailer; 11/04/15.
I am continually astounded at how quickly people make up their minds on little evidence or none at all.
Jack O'Connor