Re: Fox Sterlingworth
I have a Fox Sterlingworth with SN 5797X that according to Fox factory records was shipped October 24th, 1911 so I expect yours was shipped around that time, probably just a little later. Mine also has 26 inch barrels which is a little unusual but letters that way.
Restoring your gun could cost any where from around a hundred bucks or so to several hundred or more depending on how much you want done. And you would never get that money back when you sell the gun.
Best to use it the way it is after having someone familiar with old doubles check it over to make sure it is safe to shoot. And only shoot light field loads with lead shot.
Hard to say what the value would be as it is now. Can you post some good, focused, close up photo's?
Hope this helps.