I don't even attempt to come close to the knowledge base you guys have but I think you are right Bruce or at least very very very close.
We start with Henry P Hawkins himself, born 1833 in New York he is found in 1860 census in Patterson, Wayne County dwelling #1 listed as a merchant living with none other than William Patterson.
Ancestry.com shows him as Capt Co F. 6th Mo Cav promoted to Major per NARA film M390 roll 20.
Spot checking Co F names vs 1860 census and a common Aug 1 1861 enlistement Date of Ironton, Wayne Co shows a match on 5-6 names including Alexander Osborn Miller (b 1836 North Carolina, d: 1885 Wayne Co MO) shown on 2 cards in MO SOS file first as Pvt Co F Aug 1 1861 and then as F&S Commissary.
FWIW
John R.