I have reservations that this safe was mfg by HHM.

I have not seen it all, but have been studying and recording dial patents for almost 40 years. From my findings your patent group would indicate one of the locks below;

Yale 024, 026, 028, OB/B, & Marvin Imperial
July 25 1871
Sept 2 1873
July 28 1874
Sept 7 1880
Nov 2 1880
Nov 2 1880

It's easier to ID a safe from an interior door picture showing the bolt work mechanism and combination lock.

DH