I would suggest that anyone attempting to do something to SXS barrels on his own to proceed with all due caution. Some chemicals will compromise the solder that holds the ribs to the barrels and that's the last thing you would ever want as a result of 'trial and error'.

Thanks for all the comments and suggestions. I'm curious if it would be in my best interest to have the barrels refinished, or to clean the rust off and leave the barrels alone? There's a local gunsmith that has been in business for 40+ years, and is very reputable. Do y'all think I should let him do the job?

Personally, I'd send it to a gunsmith that is familiar with Damascus barrels. Your smith may be reputable but does he have experience with vintage shotguns, Parker's in particular plus Damascus barrels? It would be best to send it to someone like Brad Bachelder, Kirk Merrington, or Keith Kearcher. They can take care of the rust, refinish the barrels if you want, and also tell you if the barrels are structurally sound. Just MHO.

I wouldn't mess aroung with a local gunsmith. More damage has been done to Parkers over the years by do it yourselfers & experienced gunsmiths that don't understand Parkers or thier value.

Brad & the others mentioned specialize in the proper technics to repair these great guns correctly.

It will be worth every penny spent in shipping to have Brad or one of the others look your gun over & give their recommendation on how to go about saving this gun.