Gerry,
For low-velocity .375 Winchester loads, use .38-55 load data. It's perfectly safe because the .375 Win is proofed to higher pressures than the .38-55 (The reverse is NOT true!!)
The cartridge cases are almost identical except for length, and that 248 grain plain base bullet is perfect. Size it to .375" or .376" (depending on your groove diameter) and load away. A Lyman Cast Bullet handbook will list recommended loads.
I like Alliant Unique for plinking, and blackpowder for full loads. For your low velocity loads, start with IMR 4198 or IMR 3031 powders. Either one will give decent velocities with starting loads.
For air-rifle velocities, try swaged .375" round balls on top of small charges of pistol powders (WW231, Bullseye, etc).