This suggestion may be a bit out of the box. However, your situation (bad shoulder, non-reloader) narrows the playing field a bit and leaves few options.
What I'm speaking of is a sporterized .303 British Enfield. They are not hard to find already sporterized . Complete Enfields are still easily obtainable for use as is or can be sporterized. Remington and Winchester still make ammo. The .303 is more than a capable Elk cartridge with 180 gr loads.
Another reason I suggest this is the weight of the rifle, which should help with your recoil issue. I have two sporterized versions and both weigh 9 lbs. Recoil from the bench with 180 gr loads is far less than either of my .30-06's, 270's or .280's. I place the recoil at about what my 7mm-08 Handi Rifle with 140 gr. rounds is. Again, this is from the bench.
If the weight of a rifle is also an issue, then this suggestion may not work for you.
Sporterizing an Enfield is not a major event. Weaver used to make a one piece mount that mounted to the recever and stripper bridge. I reguarly see those mounts at well established gun shops and at gun shows. The bolt is already bent sufficently to clear a scope. The butt stock can be used and the forend can be cut down. Numrich Arms and Springfield Sporters may still sell cut down forends. Advanced Technologies offers a synthetic stock set. However, I'm not sure what that drops the weight to. Head space is generally not an issue because the .303 headspaces on the rim. At any rate the bolt head can be swapped for a longer one.
If this suggestion is a viable option, feel free to PM me for details.
Just this weekend I came across a sporterized .303 at a shop that was not butchered. It still had the original sights. Only the wood was removed and the forend shortened. The asking price was $100. It was in real decent shape.
The same could occur with Mod 24/47 Mausers. They are relatively inexpensive these days. I have read, however, that factory 8mm ammo is loaded down to near .30-30 specs. If so, then not being a reloader, this would be an issue.
The top model has a Fagen stock (no longer avaiiable, but Boyds offers something similar).
The bottom has cut down original wood.

Again, just a suggestion.
Thanks.