The only real reference I have ever seen for these cartridges is contained in the book cited in post 14 of this thread: What to shoot? "U.S. Cartridges and Their Handguns"
by Charles R. Suydam. There is a typo on the .32-44 page, it shows the cartridge as the .33-44!
Either .32 S&W Long (If you don't mind some case bulge.) or .32-20 brass could be trimmed to 1.00" and used in the .32-44. Based on listed dimensions for the .38-44 the .357 Maximum case will probably work for this one when trimmed slightly. The .357 Maximum is ca. 1.600" while the .38-44 is 1.480 +/-.
Note these cartridges are described using - between the elements instead of a / as when describing the 1929 .38/44, at least in common practice.