While applauding your enthusiasm, a "like it left Fulton" restoration will cost up to $2000. Refurbishing is a more reasonable option.
Please check the first question in the "Maintenance and Restoration" FAQ on the LCSCA site
https://lcsca.clubexpress.com/content.aspx?page_id=274&club_id=43784If you'll let us know your general location, we might be able to recommend someone near you.
Does the gun have a HOT? There are very few smiths able to work on HOTs; Jerry Andrews is one.
Please be aware that Hunter Arms did not lengthen the 20g chambers from 2 1/2" to 2 3/4" until about 1936.