If I were purchasing a dedicated big game rifle I would also go 30 cal or larger in order get some separation from your 270. The WSM may offer some advantages with regard to rifle weight if that is a consideration.
I have fired the 300 RUM and its recoil is strong but not as bad I expected. In fact there are several reduced power offerings from 30-06 to 300 WM to 300 RUM. Thismay allow you find your comfort level. Not to metion next time you go shooting you can shoot 150 grain 06 loads, and slip in a 200 grain full power RUM load when you let you buddy shoot one.
