...I've long been a proponent of muzzle blast & poor position being the culprit in "felt recoil" (& "scope eye"), more than the actual recoil, itself. Ear protection, even double, a good cheek weld, & your body position from the bench should be al most the same as your offhand position, upright...
...if you're considering the Axis (too many returns @ the store), I'd think about spending just a little more & take a look @ either the Mossberg or Marlin compacts, better buys IMHO. I think the Ruger is better & worth the money. Tikkas are competitively priced, & offer a lot more for features...
...mule deer rut around here doesn't really get going till (mid) Nov., most of the bigger bucks tend to stay higher, good chance of snow in the Bighorns in Oct., but most of the rds. should still be open. Sounds like you've got a Region R tag, a lot will depend on where you're basing out of...
...I've pretty much forgone H110 & 2400, using Lil'Gun instead, generally better MV w/ less muzzle blast, cleaner burning, & relatively easy to find...
...a lot of things go into altitude density, colder air is thicker, higher elevation is thinner, 50% relative humidity is a lot less water vapor @ 40* than @ 80*. Consistency is a hallmark of accuracy, but might there be a line that stepping over bogs us into "anal retentive". For most hunting...
...plenty of inane comments from both sides, but the all seem to miss a major point. "It's the same old story, same old song & dance, my friends", I happened to be working for the State of Idaho during the original implementation of the "Grizzly Bear Recovery Plan". We spent months in meetings...
...the WYG&F gives outfitters "crackers", but tells everyone hunting that the grizz consider gunshots to be a dinner bell. Sometimes all you can do is shake yer head...
...a number of trails in the Cody area, not Yellowstone, not the Recovery Zone, are already closed due to "bear activity", bears, mostly sows w/ cubs are being trapped on the golf course, in subdivisions as they move lower down the river systems to protect their cubs. Conflicts are increasing...
...sounds like you are going to be doing some management activity, get w/ your county agent, see if they have a "wildlife" reseeding mix you can throw on skid trails, landings, etc.
...a rag soaked in rubbing alcohol laid on the barrel works pretty well, evaporates & cools faster than water, doesn't rust, just need to lightly oil after shooting...