Show us this rifle that kick to much...

It's also very interesting how much stock design plays a role in felt recoil. My brothers remington 7400 in .270 had more recoil and muzzle flip than my winchester featherwight with the same ammo.

More than one person was surprised at the difference.
 
I have a Ruger No.1 in .358 Norma Mag and that is the max end of my recoil tolerance. I can handle it, but I'm not interested in anything bigger. And I hate to say it, but smaller cartridges will do the job 99.9% of the time. I have a Ruger compact in .260 Rem with a 16" barrel that I could shoot the head off a grasshopper with at 100 metres that would certainly takedown anything from a moose on down. There is still something awe-inspiring about that .358 Norma though!
 
For the OP the only thing that I would do is load that .500 down, good 500 to 700 grain bullets (cast) are not expensive and when driven 1100-1200fps should be all you need for paper punching and big game. What kind of throating do those rifles have?
 
In mine, the throat's long. With the 700 gr bullet I use:

OAL 2.575"

IMR4198 - 40.0 grs (full) - 1450 fps
WC-735 - 50.0 grs (slightly compressed) - 1550 fps
BLC-(2) - 48.0 grs (full) - 1200 fps
 
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