Your serial number tracks to 1922, so the 12/21 barrel is probably original. However the C stock was introduced on the 1903A1 which started around 1929, so it's probably a restock. The lack of cartouches could be from the refinish.
As for the "black" finish. Is it paint, phosphate (parkerized) or what?
I don't know why this would be associated with the CMP. They don't normally "refinish" anything.