A .375 JDJ type on a No.1 MKIII was always a "want to do" of mine. Again, the JDJ is proprietory and the guys who have the reamers don't have any interest in the idea. I have a Martini-Enfield on the way home from having the rotten .303 bore bored out to .375 and the original .303 Brit chamber neck reamed and throuted so I can just neck up the .303 cases to .375. It doesn't have the capacity of a JDJ, but should be close to the .375 rimmed express. I believe that with the 21 inch barrel, I can still push a 250 grainer at about 1800 to 2000 fps. This will be my own ".375 Nitro Express". I will let you know how it works. It is not the fast and sleek LE anction, but, then again, I don't need to be concerned about feed issues with a single shot.
I have seen on this NE Site, a gunsmiths examples of No.1 MKIIIs with the charger bridge removed and the stocks done in the patern of some old fine English guns that would make anyone drool. I would love to find this again to have one done in .303 or any workable caliber. I have seen a .35 Win. at a local show a few years ago. I past it up because I didn't know how it would feed and function.