Are you sure about that? At that time the U. S Army was using the Benet-Mercier (AKA the Daylight Gun), the Lewis Gun (in .303), and a few M1904 Maxim guns. I am not sure if any of the M1904s were used by the Punitive Expedition, but the other two were.

"Does anyone remember the Cadillac Bar in Nuevo Laredo? They had Pancho Villa’s saddle on display. (It was heavily worked with silver.)"
I spent lots of time at the NL Cadillac Bar in the late 80s and early 90s while I was living in Laredo, but I don't remember seeing any saddles there. But I do remember stories about Pancho riding his horse inside, true or not I don't know. I think the Cadillac has been closed for a long time due to the Narco violence in Nuevo Laredo, and also the fact that very few Gringos dare to visit NL these days. It used to be a good place to take a walk around the downtown area in the evenings, and I would cross over two or three times a week to do that. And also to watch the Border Patrol search cars at the U. S. side of the bridge. No way would I go to NL (or to any border town on the Mexico side) now. There was also a Cadillac Bar in San Antonio near the River Walk, but from one visit there some years ago it was nothing like the one in NL. I don't know if it is still open.