Charles:
The way you give us these details, tells me you find the serial number listed in the Price & Fjestad serialization book.
Considering the era and details you tell us about what you are holding, it feels unlikely the serialization book has that many typos! It’s not likely to have typos about three (3) things: the barrel steel, the gauge and the barrel length!
So, apparently somebody hand fit new barrels to it.
As for the numbers stamped on the barrel, well… people that have stamps are going to be stamping. Too early to say whether that person was working in the factory or a fine quality custom gunsmith.
Now, were the new barrels fit by the Parker Brothers factory? Or someone else?
I notice that the new barrels are marked as Titanic Steel. Since that is the appropriate fluid steel for a grade 3 gun, I can’t think of any place it would be easy to get, unless somebody were working in the factory. Not impossible for the after factory gunsmith to get, but that calls for a little more patience, cost and attention to detail than the average gunsmith has (or maybe they just got lucky).
If this were mine, I’d post pictures of the relevant areas of the water table, barrel markings and barrel flats. Then ask the good folks that visit here to opine about whether it looks like factory work or not. I feel fairly confident that the consensus response will be a solid answer to the question. Not definitive, but solid and reliable.
I’d also submit a research letter request. Considering you find the number in the serialization book then it feels highly likely you’ll be able to get a research letter. Until that letter is done, it’s too early to know whether or not an order book will be available to give the definitive answer about a barrel refit at the factory on this gun. You’ll only know when you ask.
One more thing I would do is post in the lost and found portion of this board seeking the Damascus barrel version for this particular serial number.