I have used IMR 4198 with the 220gr Hdy's in my Marlin over the years with good success (1' groups at 100 yards w/ a Leupold 2.5x scope with heavy duplex reticle).
I have also used the Winchester 200 gr FP ammo too.
HSM ammo now makes 375 Win ammo loaded with the 200gr Sierra bullets, and is priced better than the Winchester ammo (which they finally produced another run of) $57 vs $80/box. I had P&D in Edmonton order it in for me. I recently saw both brands on the shelf at Corlanes in Dawson Creek.
I have some of thee Sierra's on hand now, but have not tried a load with them yet.
If my 94 Big Bore likes the HSM ammo, I will try developing a load for with with the Sierra's and keep my Hdy's for my Marlin.
I have taken a fair number of moose and black bear with the 375 Win over the years (since 1996) and it has always performed well on big game for me out to 130 yards. I have also harvested one caribou with it. It will be my first choice when I finally get to go on a cougar hunt! Love the 375 Win!
As noted above; be careful with 38-55 ammo/brass. You can safely fire the 38-55 ammo in your 375 but you do not want to fire the 375 in a 38-55 rifle. The 375 is loaded to higher pressures as the brass is thicker and can withstand the higher pressure. If you were to use 38-55 brass for your 375, DO NOT LOAD to MAX!
There was an ad on EE recently for 375 Win brass.