Hooligan1, a 200 grain at 2800 fps is more recoil than a .30-06 pushing a 180 at 2800 fps. That's about all I can say about the recoil other than it is less than my .375 Ruger pushing 270 grain bullets at 2800 fps. I know that isn't much of an answer but it's all I have.
For medical reasons if you are interested in a .338 I'd look at the .338 Federal. Of course you could load down the .338-06 to the Federal levels but what is the point of that. However you can push 160 to 210 grain bullets to very respectable speeds with the Federal without punishing you too bad.
Too bad you aren't any closer I'd loan you my 1903 to try.