carpediem
If you can get the "Cast Bullet Supplements" from the NRA they would provide you with a wealth of info on cast bullets, particularly the .375. There is an excellent article on using cast bullets in the .375 in Africa.
I have been working with Lyman 377449 which is a GC design. The bullets weigh 270 gr gas checked and Javlina lubed with the alloy I use. I shoot this bullet at about 1800 fps just for practice. I cast these out of WWs and have been using AA5744. For hunting I use new "magnum" shotgun shot (size doesn't matter) that contains about 5% antimony. I drop these out of the mould into a large coffee can of cold water to harden them. This anitimony/lead alloy will harden to sustain about 2200 fps and yet give expansion instead of shattering like antimony/tin/lead alloys. I have been working up a load with 4895 and a dacron filler that shows real promiss at 2100 fps. While not up to standard .375 H&H velocities it exceeds the power of the .375 Winchester. I wouldn't have any problem hunting with it.
For grouse, ptarmigan and hares try the Hornady .375 RB tumbled lightly in Lee Alox lube over 4 gr of Bullseye. It will run around 900 fps and is accurate enough for these small game out to 50 yards. And they are just plain fun to shoot.
Larry Gibson