I'm not finding any further information on Jas. McCulloch, the owner of the gunstore who made the original order with Parker, but there is a lot of info on the 2nd owner, Rufus K. Dryer, who sent it back to the factory to have the chokes opened up...
Rufus was a very prominent banker in Rochester, and an avid yachtsman / outdoorsman. He died in 1937, aged 91, and was survived by his son Joseph, who was a bond dealer, also in Rochester.
Joseph had a son, also named Joe, who went to Dartmouth in 1940. There he became friends with Jack Hemmingway, son of the author. They joined the Bait & Bullet club, and shared the two arms that Jack had brought with him to school, a Winchester Model 12 SN # 600296, and a Remington pump-action Model 14 rifle in .44 cal, SN # 96674. The shotgun had been a gift from his father, but the rifle had come from a gunrunner friend in Florida.
Jack quit Dartmouth to join the Army in '43, leaving the two guns with Joe, who stayed to graduate. Joe then became a 90-day wonder Lieutenant in the Marines, and was wounded on the first wave at Iwo Jima by a sniper's bullet to the chest. He recovered after a year in the hospital.
A few years later he moved to Cuba where he and his brother had purchased some land, and there he had the occasion to meet his old schoolmate's father, Earnest. Joe told the tale of his knowing Jack, and that he was still in possession of the two guns, which Earnest never bothered to retrieve; they are reportedly still in the Dryer family.
While the broken Parker likely never came out of his grandfather's or his father's closet to have any association with a Hemmingway, I'm pretty sure that it would have been Joe, the USMC Lieutenant Purple Heart recipient who would have sold the shotgun to Uncle Bill. They were about the same age, and were both WWII veterans living in the same town. Who knows, perhaps they met at a smoky VFW hall, or at one of the clubs shooting clays. We'll never likely know, but I'm for one sure glad they did meet.
I got the data on the second Joe from two sources, a newspaper bio on Joe, and this book:
Hemingway's Guns: The Sporting Arms of Ernest Hemingway