Sure, a larger cartridge leaves a larger hole there is your proof. This is not to say you need a cannon, but I would go with someone who is a professional i.e. a guide over your "message board" advice.
That's not proof, that's an opinion....
"If" we are going to use "opinions" for "proof", why would YOUR opinion (you say you've never hunted a big bear) be more accurate or of higher value than MY opinion???? Ihunted brown bears for over 20 years, harvesting several myself, andwas in on hunts where many more were harvested by others?????
At least i have some "experience"and knowledge to back up my "message board" advice....
BTW, a .308" 200 NP out of a magnumwill bust a bear down just like a .338" 250NP will.... I never used the 30 cal. 220NP's, but i suspect they will work just as good or even better....
DM