Sling Pad, Lighter Bullets
I have a 8x57 mauser and that thing kicks like a mule when I load up to full power (like the european loads). I put a recoil pad on first - that was cheapest. And since I built it from a barreled receiver it also sports a medium heavy wood boyd's thumbhole stock - nice feel to it. Lastly I have had the front sight removed and had it ported. Didn't reduce the recoil as much as I thought it would but it wasn't an aftermarket muzzle brake - probably wasn't large enough.
Shooting prone or bench is very accurate but also puts all your weight behind the rifle's recoil. It has no where to go but into your shoulder. If your practicing for hunting you might want to try posting up. Shoot standing up with the rifle resting on the side of a post (more like what you might be doing when hunting) - the recoil will bump your shoulder backwards instead of hammering you as you "lean into it" on the bench.
I also have a TC Contender rifle with a very light choate stock on it in 45/70. This is probably a 7lb rifle. That kicks worse than the 8mm. And the Choate has a terribly blunt butt end. I bought a recoil pad sling to use at the range. This is a heavily padded leather shoulder pad that you can put on over your t-shirt (or anything else) when at the range. The sling holds the heavy pad right where your rifle rests on your shoulder. It's great!! In winter with a heavy coat on it isn't needed. I always take it to the range when shooting the 45/70 or the 8 in summer. And it isn't attached to the rifle so I can use it on anything. I also put a mercury recoil tamer in the buttstock, which also helps a bit.
Another thought is bullet selection. If you shoot 180-200 grain bullets near max load then that is going to kick hard. If you switch to 150-165 grain bullets at medium velocity you will notice a difference. Usually if your target shooting, I have found that the sweet spot for accuracy is around 2500fps for a lot of different bullets (150's-180's). If you reload you can reduce the powder to make a comfortable and accurate round for target. On the other hand, if your target shooting to work up that elk or moose round your going to be working for it on the recoil side (heavy - fast bullets for penetration). Might want to eventually get a brake or get a combination butt pad and a sling pad to start.