The 375 Win has worked very well for me for black bear, moose and caribou over the years, in my Marlin. Call it "Thumper" as every black bear has thumped the ground promptly. One of my favourite bear hunting cartridges! Best of luck with yours!
Have used the Winchester ammo with 200 gr Power Points on all of these, and it has worked very well.
Have also owned a few Winchester Big Bores over the years, and have just acquired another one.
Winchester made another run of ammo last year and there is some on dealers shelves currently. They are running about $90+/- a box, dependent upon the dealer.
HSM is also making ammo with the 200 gr Sierra bullets, and is better priced, if you can find it. I ordered mine in through P&D in Edmonton. Will try it in my new-to-me BB when it gets here.
I also handload, and the 220 gr Hdy FP over 32.2gr of IMR4198 produces 1" groups @ 100 yards in the Marlin with a Leupold 2.5 scope with heavy duplex reticle.