Late to respond here but I concur it's musclewood, around here often called ironwood. I've picked some up from time to time and like you noted never big (maybe 4-5" dia. max). Great firewood but rare for me to ever get enough of it.
Pic was taken Sept 2020,,,,,,been outside ever since, laying on the porch bench as I remember LOL No treatment. Oils react poorly with synthetic rope. They were temporary replacements for the hard rubber and then hard plastic rollers I had previously (bow rollers) for boats. Both eventually failed from rope burns. These were only supposed to last a week, keep me splitting while I waited for some new plastic ones to come in. Previously I did not wrap the rope one turn around the rollers hoping to reduce friction wear on the rope. In the end I think the wrap is better. Bought the new splitter with normal log lift so this contraption is no longer in use.