Ken Waters came up with a wildcat he called the .375 Express. It is, in his words, "meant for the guy with a shoot-out .303 British Enfield who'd like to rebarrel it to a larger caliber taking heavier bullets, or maybe his friend who is building a new single-shot rifle."

There is a reprint of an article Mr. Waters wrote about the cartridge in Wolfe Publishing's "Big Bore Rifles and Cartridges", 1991. It includes a copy of the chamber drawing with the initials D.J.L. and the date 1979. The caption to the drawing reads, "Case design and dimensions from Ken Waters, based on the .444 Marlin case. Chamber dimensions from Keith Francis." Case length was 0.24 inches shorter than a .375-.303 so he could load heavier bullets. For the subject of the article, Waters rebored a Westley-Richards rifle to give it "a new life of usefulness...using the original barrel".

Frankly, it looks a lot like the well known and well established .375 JDJ. The JDJ cartridge might suit your needs.