Much smarter people then me will chime in here. That said the phrase "it depends" kicks in. If minimum barrel thickness of say .022 is located about 6-8" from the ends of the barrels that wouldn't both me much because the pressures have dropped way down by then anyway, and I'm assuming you would want to handload or shoot something like RST Lite loads where pressures are kept way down. That same .022 sure wouldn't work for me say 8" from the breech. I think halfway down the barrels you'd like to shoot for minimum of .032. Some factory small gauge Parkers were struck quite thin towards the ends of the barrel before the chokes started to kick in. PS. I had Fox early Pin Gun I purchased with some pretty significant outside pitting on the barrels. Had Dan Rossiter strike the barrels to remove the pitting and he had to take them down to .025 about 6" from the barrel ends before the rust blue. He recommended I only shoot RST ammo out of it but thought the barrels would be fine. When they get real thin they can be prone to dents from hitting just about anything (car doors, trees, etc. Ask me how I know :( )

It looks like this gun may have been ordered with 2 7/8 inch chambers. There were a few 20's made on the 0 frame with the long chambers. The ones I have seen went to the west coast. The barrel weigh is also on the heavy side. While your measurement of the OD diameter less the inside diameter is a good sign, the barrels still need to be measured with a barrel wall thickness gauge. IMO, the ribs need to be removed for this restoration to be done correctly. I would say the odds of saving these barrels has gone up.

Minimum wall thickness up in the front is one thing. And your pitting towards the front of the barrels looks workable. And if you are really running high 30s for thickness up there then that should not be a problem in having material to work with there. The more important thing is how much material there is back by the breech. And that is where the pitting looks worse. I like to measure thickness at the forend loop and also in front of the chambers. I like to see thickness of .050 plus at the loop and usually wall thickness will be .090" to .100" at the chamber front on most barrels.

At this point it is all speculation since only a hands on analysis of the thickness in the pitted areas as well as depth of pitting will need to be done on your barrels to know for sure.
By the looks of it, they likely can be saved. But it will be a lot of careful draw filing.

I would not try to turn down the outside of the barrels in an effort to reduce the pitting and rough spots. I would have the pits filled in by micro welding. Consult some of the craftsmen on this forum such as Brian Dudley, Brad Batchelder etc.

The verdict on these barrels cannot be rendered on this site. Although they seem savable, only a professional double gun barrel man can make that determination.

In my view, there are two good choices in that regard: Kirk Merrington or Brad Bachelder.

Since these tubes are fluid steel, some pits might be weldable. File work should be kept to an absolute minimum in any case.

Rather than elicit more speculation, I suggest you send the gun to a pro. Then heed his advice.

Not a Parker but this is my early LC Smith Syracuse extra heavy Quality 3 10 gauge with 32" barrels that had heavy pitting near the breach. The work was performed by Brad Balchelder who used laser to weld under magnification. Call him and I'm sure he will explain how he did it since I am not sure exactly how he did it. In any case, to do this on Damascus barrels is amazing. I'm sure he can help you with fluid steel barrels too.

http://i1210.photobucket.com/albums/...0110804_11.jpg

http://i1210.photobucket.com/albums/...psfa3b9ecf.jpg

http://i1210.photobucket.com/albums/...ps7e7db17b.jpg

Yes, Brad does this work on Damascus guns, as does Dale Edmonds ( through another gunsmith). I have previously posted pictures of welded splits in Damascus and twist barrels and filled pits. Some of the welded seams were quite old, indicating this repair technique has been going on for a long time. and holding since then.

Some people believe that only fluid steel barrels can be repaired by welding pits and implying that if Damascus the pits or even splits could not be welded. That is not the case from what I have seen.

BD:
Mia culpa. Being a ferrous metal composite, of course Damascus can be welded. But with varying aesthetic success by amateurs. Bachelder does well. As do a few other specialists. And... if you were to read my previous post carefully, you will find that I did not say anything about Damascus barrels, nor the potential for their welding.

Brian,
You could always just stabilize/remove the rust, get a stock on it that fits you, and have it cleaned/checked out for safety by one of the good Parker smiths here , and have the coolest shooter grade gun in the woods . It would always have the story to tell and be preserved for a full correct restoration in the future if you wanted to .
Awesome gun and horrible it ended up this way .
Great find !