Here's an interesting thought: Out of the 20 total Little Joes built, GE had built the last six of them to standard gauge when it started becoming apparent that they weren't going to be shipped overseas. One of these final six was numbered GE-750 and sent to the Milwaukee Road for tests. The initial tests weren't very successful, and the locomotive was sent back to GE.
Following that, the South Shore bought its three Joes, and a railroad in Brazil bought five of them. When the Korean war broke out, the Milwaukee saw a surge in traffic and immediately bought the remaining 12 locomotives from GE, most of which had to be re-gauged and de-Russianized.
So, there's a chance that one of the Joes may have operated on both the South Shore and Milwaukee Road during its lifetime. It seems the former would have purchased whichever locomotives were in the best shape, and since the unit used to test on the MILW was already correctly gauged and had recently been used, it would have been a logical pick. I can't find find any definitive roster for the Little Joes, but it seems like it might be possible.