I guess I wasn’t supposed to reply; if so you can do a second concluding post. I would guess the second barrel was made later and serialized to the early gun. Does it have a date code, black powder proof, or early chamber marking?
Following Sauerfan, they were some Herstal address barrel in 1903 but mine has acier spécial instead of cockerill steel on it and the barrel extension appears to have been changed. I would say that you’re right it is a later barrel.