Hmmm,
If you are use to the comfort of shooting the .270, you are going to be in for a big, and very unpleasant, surprise if you go to a ridiculously large caliber like the .375 H&H. It would be a total waste of money.
On the other hand, you will have all bases neatly covered if you go to the tried and true .35 Whelen, or maybe (maybe) a .338 Winchester mag (which I also think is way too much.)
The best advice I can give is this: see if you can find some folks who have a .35 Whelen, and a .338 Win. Mag, that will let you shoot a half of a box from the bench at your local range. (Also, if allowed, fire a half a box standing up next to the bench.) Shoot the Whelen first, then the .338. After you do this, you can pick which one you like best. (I'm betting the .35 Whelen).
If you find that both of these are just too much recoil, then check out the good old .300 Win Mag.
A practical question: do you really think that in your lifetime, you are going to spend $20,000 to go to Alaska and shoot a big time grizzly? Or, spend that $25,000 (or more) to go to Africa and shoot a Rhino or a Cape Buffalo or an Elephant? I mean, . .. . really? If the answer is no, then the .35 Whelen has you covered, and the .338 has you more than covered. (Even the comfortable shooting old .300 H&H Mag would do fine.)
Regards,
Mannyrock