I'm not sure about the rib. How will the barrel affect the value of the gun?

Looks like Remington work to me.
The barrels may have come from Meriden stock and fitted and stamped by Remington as replacement barrels.






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We have seen a few late Remington barrels with choke markings before. The repair code looks like it is DW3 which would seem odd as W for a year code was 1928, 1972 or 2002, all out of the time period Remington would have been doing repair work on Parkers. Could what appears to be W be YY which would have been 1950?

The MADE IN USA marking has been seen on several Parker barrels from the era around 1937. Perhaps Remington only used that mark on replacement barrels in that era.
The choke markings are also noted on many Remington era guns.

If Remington put the barrels on the gun, wouldn't the repair code end with a 2 rather than a 3?

No.

And many barrel sets were stamped with the circle but not the type of steel inside it until the grade of the gun they were to be fitted to was determined... plus the fact that Remington didn't stamp the steel type after the move to Ilion.





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Better pictures of the Remington repair codes are neccesary. Many pictures of the entire gun are neccesary. The forend pictures suggest a really bad refinish and bad wood to metal fit. The choke markings, and the circle are completely legitimate for barrels installed by Remington at whatever date is stamped on the flats. Where are the rib pictures?

It would surprise me to see a legend on the rib.





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Looks to me that the serial number may be stamped on the flats in the shadow under the "FULL" stamp. It also appears that there may be a second repair code "WD3" below and to the right of the "DW3" repair code. This would mean August 1935.
Brandon could slow down a little on asking about effect on value and be a bit clearer on all the markings. This would give answers to his question greater validity based on complete info.
No photo or info on what is stamped on the side of the barrel lug but I would expect it to further verify Remington re-barrel. Barrel steel is marked on side of lug if I remember correctly.
Erick