Here's another one for your suspected Buckman list--the only Buckman-like engine I have left other than a fire pumper. Known to me only from this page in an 1886 FAO Schwarz catalog (description but no illustration, same page as the better known "Ajax" engine). "Empire" of course is only the model name which is also cast into the cylinder. The burner is borrowed from a Russell Frisbee engine from the same period.
Forget about the Smithsonian engines. I viewed them over 20 years ago in storage when none were labelled or photographed. I offered to identify them at the time but there was no interest. It's even worse now as the curator in charge of mechanical engineering is a marine archaeologist! Identifications and photos being posted now are probably the work of volunteers.