Ron,
I think 8194 is the order number that was found on the barrel flats. The serial number will be on the left side of the barrel lug and should match the forend and trigger guard bow numbers. Gteat looking old Parker and a nice find. I have two lifter Parkers from 1881 with Twist steel barrels that I shoot often. I do think your barrels have been cut as it appears to be no solder between the ribs at the muzzel. I would not replace the stock. There are many good people that can repair it and you would not be able to find the repair.
Go ahead and clean the barrels. I fond one full of old black powder soot once and when it was cleaned I was supprised to find it shiney. The surface rust on the outside can be removed with Hoppe's 9 and OOOO steel wool. Just work lightly and in small circles and the rust will just wipe off.
Kindest, Harry
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