Snakeman, I would say that the 357 magnum loaded stiff and heavy as other have suggested is adequate for the job. You are the hunter, possibly guided by a guide and you’re not making your living at bringing home elk daily. But as crazy as it might sound there are a couple old guides still packing a 357 in a very strange way.
I read this article once and have no source, yet it was interesting reading. It was about an Alaskan guide a few days into an elk hunt in bear territory. The hunter was questioning the guide about the guns he was carrying, and the guide said a short levered 45/70 and a 357magnum.” What, just a 357?” The hunter said. The old guide said “yah, that’s right, just a 357”.
The guide said it was something he learned from another guide; the only guide he ever knew that was mauled by a big grizzly and lived to guide again.
The hunter said, “What’s that got to do with you carrying a 357?”
The guide pulled out his revolver and emptied all six carts and said “there all 110 grain HPs!” “110 grain HPs?” The hunter questioned! The guide pulled up the 45/70 from its scabbard and said “it’s all about range”. “ If the bear is going to charge, this is my back-up, if something goes amiss and it can happen, just as I am being mauled I will empty every last 110 grainer in the grizzly’s skull. The guide said “yep it’s all about range”.
That article sent chills. This guide took his job very seriously and had his survival right down to the last few seconds.
In your case, stay with 180 BB.