A very popular option is to get a Marlin 336 and send it off to JES for a rebore that takes a 38-55 or a 375. His rebores are supposed to be 376 and take about anything available for the 38 bore. Barnes is starting to offer their OS 38-55 bullets in 375 and 377 diameter. And there is another maker of J bullets people are happy with Vollmer Bullets. Lead bullets are also available as are molds. I like the Lee 250 grain mild and the Lyman 264 with gas check. For close and dirty work the Lyman gas check mold would be the ideal.
I don't know if a standard 94 action would take the 375 but many were made in 38-55. I believe the Big Bores were beefed up actions. I shoot the 38-55 quite a bit and enjoy the caliber. The Barnes OS bullets were effective on deer.
DEP