I'm not quite there, but its getting close! I drove rig-up trucks/moved drilling rigs/30 ton tandem, rigging,etc for 20 yrs in my early adulthood. No automatic transmissions, all 4 speed Brownlight and 5 speed standards, reach around and work winch levers, etc) Replaced both knees, left hip ( yep, my clutch leg/knee!) plate in neck. I can take alot of recoil, but I am noticing some subtle changes in my right shoulder. While it isn't freezing up, etc, it gets sore; some days worse than others. So, for the bad days, I am thinking of a lighter weight/lighter recoiling (muzzle brake is fine) but not ultra-lightweight ( I can't shoot them well) rifle for elk. (I was thinking the Kimber Pro Hunter Dissolve in 280AI or '06 w/brake might be too light?) I limit myself to around 300yds anymore also.
For hayfield, etc cow elk, I have a sweet older Mod 700 25-06. I am scrounging up an older Remington 700 Model 78 30-06 that has been set in an older wood, ADL stock. Limbsaver and a brake would do nice. I like the older Model 700 Mountain Rifles and of course the older Mod 70 FWT. Anyone travelled this route for this reason?
Tikka fan here. I would take a Tikka T3 and suit it up in a caliber that works for you. A 30-06 would be plenty, the 270 would be good. You could even take the 7mm-08 and convert it to a 280 AI and be in one pretty cheap. Although I bought a Kimber Montana in 280 ai for about the same price that it would cost to make that conversion. I feel like the Tikka is very good with recoil for me. I am not recoil sensitive either and I am a pretty big guy, but the Tikka T3 I have in 300 win mag feels like light recoil than any other 300 win I have fired, much more like a .30-06. You can buy a pre-fit Limbsaver pad from Mountain Tactical and be good to go. You could also go with a .284ai and take advantage of the long magazine and chamber length that Tikka offers if that is more up your alley?
As others have mentioned, you can also tame recoil by going with a longer, lighter solid copper bullet like the TTSX.
