My report: When I said how a .38-55 cartridge would easily fit in the rifle's chamber I was using a factory loaded round. After wondering if the crimp at the mouth of the case was allowing the bolt to close even with the slightly longer case length, I tried to chamber a handload with a cast bullet which was not crimped. That fell right in. Next, trying Bledsoe's advice, I chambered a fired case that was not resized. That also chambered very easily. Next, I'll have to fire one of my .38-55 handloads in the .375 but I'm sure that won't reveal any problems. So far, I'm convinced that the .375 Winchester barrels on the Marlin rifles actually used .38-55 chambers.
Now, one reason I like the .38-55 so well is because many years ago I had a buddy and hunting partner who used a Winchester Model 1894 Saddle Ring carbine in .38-55 as a deer rifle. I was with him when he bought that gun and he paid the terrbily high price (at that time) of $135. His rifle has a Nickel Steel barrel for smokeless loads and jacketed bullets. He'd buy factory ammo and then pull the bullets, then reload the cases with cast bullets. Those were just for shooting. The jacketed bullets were saved for handloads with generous doses of Hi-Vel #2 to duplicate the old .38-55 High Velocity loads. With those 255 grain soft-points fired at about 1750 feet per second, that carbine of his would sure knock a deer down.
I also have an old .38-55 but in a Savage 99. One nice 4-point blacktail has fallen to my rifle, hit from 104 paces.
There is a practical reason why I want to use .38-55 ammo in my .375 and that is because I have a good set of bullet moulds for the .38-55. Those bullets could be used in the .375 but they'd need to be seated deeper or left with a groove exposed to be equal in length with the .38-55 loads. It is just much simpler to use the .38-55 brass. That's particularly true with Lyman's bullet #375296, a gas-check bullet weighing 265 grains. My mould for that bullet is a double cavity modified to cast one solid nose and the other one a hollow point. The hollow point bullet does quite well for hunting.
Now I'll have to see how well the faster rate of twist in the .375's barrel handles the cast bullet loads. Perhaps another report shall follow.