My 300 H&H weighs just a little under 8 lbs, I shoot 180 TTSX's and for me that's about the most recoil I can still find some joy in. Your 300 wsm should be about the same, but with the lighter barrel contour will have more"muzzle flip".
I suspect if you dropped down to say, 150 TTSX's it would be easier on the shoulder while still killing stuff dead enough.
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