Savage purchased A.H. Fox in 1929, and by 1946 all of Savage's production had been moved to the Chicopee Falls, MA location. As such the build date (possibly - see below) would fall somewhere in that time frame since the barrels are market Utica, NY.
That said, a lot of the earlier Philadelphia made Fox Sterlingworth shotguns that were sent back to Savage for warranty or repair work were often fitted with new barrels marked Savage Arms. This is because at some point in time Savage adopted a policy that any Philadelphia Fox guns sent to them for repair would first have the barrels measured and if thick enough they would rechamber to 2 3/4 inch and then proof test at owners risk before they would complete any other repairs. If the barrels would not meet Savage's proof standards the gun would either be returned to the owner or new barrels fitted (at cost as a matter of customer good will), the old barrels destroyed and then other repairs completed.
As such yours could be an earlier Philly made gun that was rebarreled. My knowledge of the history of Fox shotgun production is pretty thin so you might want to sniff around over on the Fox Collectors website and see what you can find.
http://www.foxcollectors.com/
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