"I believe Hornady no longer makes the 220grFN .375 "
No, these haven't been available now for quite some time.
Even the Sierra are difficult to find.
I am lucky that I stocked up when I did, or as I have come across it over the years, so I have a decent supply on hand to last me a while.
I was using the Hdy in my Marlin, and the Sierra in my Winchester.
When I recently sold my 94 Big Bore to a friend, for dealing with problem bears on his cabin property, I did set him up with some ammo, dies, brass and bullets to last him a while too.
Winchester did make another run of ammo a few years back, and some stores still have some on the shelves, but it isn't cheap!