Hello,
Having only hunted elk twice, you must take my thoughts and theories on elk cartridges with a grain of salt. On the other hand, I have in fact let the air out of an absolute railroad car or more of deer and caribou, not to mention three trips to Africa, the last one lasted a month and included culling female antelope to help rebalance the local gender ratios. I might know how to fix someone up with a "deer rifle" who is also recoil sensitive.
All these latest gadgets and moving parts make me nervous. I don't even like variable power scopes. Too many moving parts. (Bah, humbug to unnecessary moving parts). Having volunteered as a line safety dude on a major rifle range, just outside The Twin Cities, Minnesota, during the week prior to deer season, I've come to the conclusion that typical sporting/hunting semi autos are not overly reliable in general, including with factory ammo. The more robust Military designs seemed to be more reliable as self loaders go, reloads or not.
In today's technology worshiping culture, we Americanos tend to be preoccupied with finding solutions to firearms problems that usually have already been solved by our Grandfathers. Tolerable recoil in a deer worthy rifle is one of these already solved problems, if you ask me. Even for elk, the following information might work well. Although admittedly, it's not for truly long range shooting on such largish and potentially "impact resistant" critters like an elk.
Any way, when I was raising my wee sons (both now bigger than I am), by age 12 each, they had graduated to the .300 Savage cartridge for such things as caribou and deer hunting. Even with a 180 grain bullet, recoil is very moderate in a bolt action, lever action or even the good old Remington pump rifle. It is likely not a 400 yard elk cartridge however, it is possibly suitable out to about 300 yds if one is willing to practice, practice, practice and chose a proper bullet weight for the animal hunted. (Good advice for any choice of caliber). If a person does not reload, it is very easy to find a few boxes of live shells for it at any place ammo is sold in USA and Canada. Furthermore, it is not very expensive as ammuniton goes.
Remington made a limited run of their Model-700 Classic in .300 Savage and it was a sales flop. therefore, they are often available for not too much money. Likewise their old 1950s-ish Model 722 bolt action (father to the short action Model 700 ADL) has not had much collector's interest in .300 Savage caliber. Both models are typically super accurate and of course scope bases by most any company that makes them are very common for either model.
I will admit that there are a million other cartridges better suited to elk hunting, especially if the shots are likely to be quite long. However, most if not all of them recoil and blast like a howitzer (and ruin about as much meat sometimes as well). With a normal weight bolt action .300 Savage, the person who is recoil sensitive can still shoot a .30 bore and 180 grain bullet without any sort of ear drum blistering muzzle break needed for that once a year shot at a critter. A person does not need to risk their established accuracy by cutting slots through their barrel or from threading on some product that the inventer claims will do all things, including: keep the IRS off your back, cure gout and help you find a woman.
The 7x57 is another fine hunting caliber for low recoil and it IS in fact generally available around the world. The 7x57 is marginal for elk at longer range like the .300 Savage is but reportedly does good enough work out to "normal" ranges at which elk and deer are typically shot. However the man had mentioned that his soon to be relative has a medical problem of recoil which needed to be solved with at least a .30 caliber. If reloading were an option, I'd vigorously agree with one or more writer here on the
.30-06. That way he could load it to a tolerable recoil level and at such time as his health improved, he could start turning up the flame on velocity and recoil. For that matter, he could just do that in the first place with his .300 Magnum, if he reloaded for it.
I only hope the man pulls through his bout with that terrible disease and "comes out shooting".
Merry Christmas.
Ard