25% more recoil wouldn't bother me. I'd probably not even notice the difference.

The 300winmag I'm referring to kicks less than my brothers 14 lb 308win. that has a solid buttpad.

My guess is that your 338 LM at 20 lbs shooting the 300 grainers around 2,700 - 2,750 will feel no different than a 8 lb 308 win.