leenfield - The late Paul Mathews chambered up a .375-.30/40 some time ago in a Ruger #3, calling it the .375 rimmed.
Hi Article on it, is on page 953 of "Wildcat Cartridges Volume II" - by Wolf Publishing ISBN 1-879356-18-X Copyright 1992.

He used the .30/40 case as it was slightly longer than the .303 and was more available for him. I fully understand the use of the .303 case. He simply necked the case up to .375, leaving the taper and neck length the same in this 'ALMOST' a straight case.

In a decent action, the loads should be verty close to what they'd be in a .303 opened up.

Paul's barrel length was 26".

If mine, Given a suitable action, I'd load a 295gr. Lyman mould # 375110 with 35gr. 3031 for 1,654fps, or a full power load with a 299gr. Paper Patched bullet with 46gr. IMR3031 for 2,180fps.

A 270gr. Hornady SP with 48.0gr. IMR3031 should give around 2,200fps.

Hope this helps.