IMHO, shooting big bores from .375 on up is a matter of conditioning, ie., getting used to the recoil over time. What has helped me is starting with a lighter load, and lighter bullet. I would suggest starting with a bullet weight of around 250 grains or lighter, and over several months work your way up to reduced loads with the 300 grain bullets. Then as you find you can handle the 300 grain bullets, increase the powder charge up, until you reach your physical recoil limit, while still maintaining a safe load level.

Honestly, though, most shooters handle, and tolerate the .375s recoil very well, but as others have mentioned. make sure the stock fits you well, install a good, recoil absorbing pad, and make sure your scope provides enough eye relief.