My solution is obviously not for everyone, but I just do my own gunsmithing work, repairs, and inspections. I'm probably not saving any money, because I have invested a lot in lathes, other power and hand tools, chemicals and finishes, books, and equipment. On the other hand, I don't have to deal with incompetent people who call themselves gunsmiths, and do more damage to my guns. I also don't have to pay for shipping my guns or worry that they will be lost or damaged during shipping. I don't have to wait for repairs to be completed. Wait times for gunsmiths who have good reputations can be well over a year. I don't have to worry that the gunsmith will become incapacitated or even die, and have my gun tied up by probate or sold in an estate sale.
All of those nightmare scenarios are played out here several times every year. That said, one well regarded double gunsmith not terribly far from you is Jerry Andrews in Moundsville, West Virginia. He seems to specialize in L.C. Smith shotguns, but works on many other vintage doubles. I have never heard any complaints about his work. I bought a couple Syracuse Lefever guns from him, but never had any gunsmithing work done by him.
The pictures you provided of your barrels are poor at best, and tell us next to nothing. I don't see any crolle pattern, just what looks like surface rust that may have been blued over. The second pic is too blurry to see any detail at all. It isn't terribly difficult to tell fluid steel from Damascus, even if it has been blued over. Do as the Preacher recommended, and remove the forend, and then lightly rub a small area with white vinegar and fine steel wool. The acid in the vinegar will remove blue and oxidation from the steel in Damascus faster than from the iron, making the contrast between them apparent. This is best done in bright sunlight. Removing all of the rust and finish down to bare metal will again make it all shiny and hard to see any contrast, so do it gradually. Then post some nice clear photos of the area, along with pics of the barrel flats and the water table of the action.
If I was a professional gunsmith, I personally would not tell any customer that they are safe to shoot their Damascus or Twist guns, even though I do it myself on a routine basis. I certainly wouldn't put it in writing, simply because of liability concerns. No gunsmith has any control what loads are fired through any gun once it leaves his shop, and has no way of knowing if the gun he inspected will be subsequently blown up due to a barrel obstruction or some hidden inclusion or flaw within the barrels... and this includes fluid steel tubes. That is a judgement call I make on my own, based upon my own inspection of wall thickness, pitting, corrosion, etc., along with the research I have done to satisfy myself that sound Damascus can safely contain the pressures generated by appropriate loads. You can ask for an opinion concerning wall thickness and overall condition, but don't expect any gunsmith with any brains to give you his blessing to shoot Twist or Damascus barrels.
