There is a list of Pape’s serial numbers and dates in volume two of Nigel Brown’s British gunmakers.
If you can give the serial number of the gun and post a picture of the proof marks on the barrels it should be possible to give an approximate date to the gun and to the William Ford barrels and that will show if as seems likely William Ford rebarreled the gun rather than making the barrels for Pape.
William Ford had an excellent reputation as a barrel maker and barrel borer, but even if he made the original barrels they would be inscribed with Pape’s name on the rib