I would like to hunt for everything here in WA at some point. Black tail, black bear, elk, moose, goat, sheep. Recoil is an issue because of a low budget and my family only having one rifle for everyone. Also, I have had multiple shoulder surgeries and target shooting gets un-fun quickly with recoil for me.
Simplify the equation, realistically, the odds are against you ever getting a Washington moose goat or sheep, so set aside the money for those applications, and don't get on that track. It doesn't alter your ballistic needs much as a big fall bear can be tough nut to crack
Multiple shoulder injuries, may mean a light weight rifle as well. In a light rifle recoil goes up. I think one of the 6.5's is the way to go, with the heavier for caliber, well constructed bullets being about the minimum for bears here.
I've got a thumbhole stock, on a .338 RUM, and felt recoil seems better to me. It could be the overall stock configuration, as its a lot straighter, and i've always preferred more "classic" styled stocks. WildRose and Roy, having me wondering if I'm using to it's best advantage, but overall I like the feel of it. Headed to the safe when I'm done here to review what I'm doing.
When managing weight I think for your purposes, a long action is worth the additional weight, as it opens the door to the 6.5x284 (the parent .284 Wnchester belongs in the conversation also) the 6.5-06, or the 6.5x55
It's not if I would start over, it's how i would start over. Trial and error is a good teacher, but those private lessons are expensive. There are a lot more quality builders out there these days, I'd save pennies, sell plasma and commission one to build me one, plus a good scope, or be patient and monitor the classifieds for used one. Best wishes.