I'm not absolutely sure what it means, but the 19537 serial number stamp on the second set of barrels (the set with only one serial no.) is a different font. So I'd assume was that the original set with the others having been made around 1900 as Craig Havener has noted? I'm also assuming there are not 12, 16, and 20 ga barrels, but rather two 12's and a 16, or two 16' and a 12. I'm not seeing that wide of a range in barrel OD's, but as you say, the cell phone pics aren't the best. It will be interesting to hear from you when you have more information to share. Does the water table have the XX small frame marking? It would also be interesting to know the width across the action breech face and barrel breeches.
