I would take a 375 Winchester and run it through a 30-30 sizing die with a .308 or .309 expander ball.
This should give you a thicker neck and provide support.
Then use a 180 to 190 grain gas checked cast bullet sized to .311 and set the cartridge overall length to support the round.
The Lyman Cast Bullet Handbook has loading data
OR have Rocky Mountain Brass make you some Everlasting cases
http://www.rockymountaincartridge.com/What do you think about these options
Mike
Fun reading
https://www.montanabulletworks.com/product/303-british-saeco-305-180gr-fngc/
