Have long said for the big bears personally .338wm would be the min I'd consider, though I'd likely anty up to the likes of a 375 H&H if I was booking such a hunt. All saidI truly believe the 300 Ultracoupled with a Barnes TSX would work on a big brown. Just something about having more and not needing it is a nicer feeling when the critter bites back!

Assuming the 338wm Ruger is as accurate and gives you the same confidence as the RUM, seems like the logical choice but if not I'd take the 300RUM. 6 weeks is doable to gain a feel and find a load with a new rifle but I'd think it is to short to gain the confidence required for the task at hand so I'd be sticking to one of the rifle's you already know/own vs buying.

Good Luck