What model is the gun? Barrels can be easily obtained for many of the newer Remington pumps and autoloaders, and if the gun is otherwise in good shape that might be a possibility.
If the barrel is really pitted, I would not suggest reaming it; it is not hard to cut right through thin shotgun barrels, and in any case, reaming would probably take the choke out of it.
FWIW, the serial number requirement was part of the Gun Control Act of 1968.
Jim
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