You should be able to use .375 Win cases. The only real difference in dimensions is that the .38-55 case is supposed to be a hair longer. Posters on various boards report that current production .38-55 cases are shorter than nominal and very close to .375 Win length.
If I had to guess, the failure to chamber mentioned earlier was due to a throating issue since the .375 case is the shorter of the two.
I will put in a disclaimer that I have researched this because I was considering a .38-55. I neither own nor load for one. I have checked the case specs for both cartridges, followed the topic on various boards, and read the available reloading articles including Ken Water's articles in Pet Loads. These sources are unanimous that the loading dies are interchangeable and the case differ only in length and weight.
That said, the current NEF rifles are far stronger than is required for either cartridge. I would be perfectly willing to load .375 Win cases with .375 data and a .378 or .379 diameter bullet for use in an NEF. I would be willing to pull the .375 bullet from factory ammo and replace it with a .378 bullet. In a pinch, I would be willing to use factory .375 Win ammo, throat and bullet seating permiting, but I would expect accuracy to suffer somewhat. (Maybe not much. My .311 7.62x39 gives acceptable accuracy with .308 jacketed bullets. Cast bullets that much undersized would be hopeless.)
I would also be willing to use new name brand .38-55 cases with .375 Win loading data. There is no telling about the strength of older cases, but no one making both cases now is gonna make them different in anything but length and headstamp.
