Lots of questions. Yes you can save a stock by soaking it for a while completely submerged in acetone. It will draw the oil out. Then you can refinish it as you like. For the barrels try using a pot scrubber from the dollar store and go over it with that and good fine oil. You can use 00 steel wol as well. You can also try an old school method. An old trade process for polishing metal used white black-board chalk sticks in combination with oil. First coat the barrels with a light film of gun oil or KleenBore Formula 3 Gun Conditioner. Then rub the barrels with the chalk stick, focusing on the rusted areas, but to include the entire surface. The rust is lifted by the chalk sticks without damage to the damascus pattern. Wipe clean with a soft rag and repeat as required until all the rust is removed. To have them refinished in B&W I would recommend Keith Kercher
Double Guns and Gunsmithing: Kody Kearcher Restorations
shooting it has been the basis of debate for some years. I myself will not shoot them..