I'm not sure if I can help you but I can give you some advice. Now this case is quite unusual because if they were living in the U.S. in the early 1900s then they were probably some of the first Ethiopians in the U.S. Most Ethiopians began to come to the country near towards the 60's and 70's (in the beginning) and before then it was unheard of. Now if they are truly from Ethiopia then they had to get in the country somehow (most likely a boat) so I would check with Ellis Island (on the east) and for the west I think the Island is called Angel Island? These were ports in which foreign people would come to the U.S. It would also be beneficial if you had there names(first names). Their last name seems strange though, it is not a commonly used Ethiopian name (obviously) and it also doesn't seem to be a variation of another name.
At the same time I also wanted to let you know that in the olden days people used to refer to themselves as Ethiopian to say that they were from Africa or that they're black. I don't know until what point people were doing that, but this could also be a possibility.
There's not much else I can say but I wish you good luck in finding out about your ancestry.