That is a great gun for the money. The wood is beautifully original. Great clean checkering. The frame is nice with good traces of color in areas. Look at the original blue on the inside of the guard bow.
To me the barrels look possibly to be refinished, but it is really hard to say for sure. There are a few things about them that jump out as suggesting that.

I don’t believe this gun has seen the light of day for a long time. If you look at the muzzle and the breach ends of the barrels, those areas can reveal telltale signs of a refinish. It’s almost impossible not to disturb those areas when doing a Damascus restoration or even a slow-rust job, such as buffing and the removal of patina.
I have an original Damascus GH 16 gauge that was supplied by Parker Bros. to the 1898 Boston Show. Aside from the grade of Damascus, the condition and appearance of the barrels on the two guns look very similar.
As always Brian, I appreciate your insightful appraisal.

Actually the look of the breech face is what is suspect to me. A factory gun should have the breech face polished off bright. On this gun, the damascus pattern is visible on both sides in spots. That is not typical of factory finished barrels. Also, the barrels are completely void of any real signs of wear, which also suggests that they may have been refinished at some time. But, maybe not. It is just observations on this fine example of a DH.

I would have thought that gun would be in the 3k range. Amazing times!

I can't comment on the Damascus patterns on the breech face, though photo forensics are interesting. I submit a possible area of not so recent staining or corrosion. Surely this would have been remedied if refinished. Without having the gun in hand, steadfast observations are difficult at best. There are other small areas of staining and also some scratches in the barrels finish.
Something to consider when evaluating is; Do all of the parts show consistent wear? And if not, why? All in fun...

Interesting times indeed.

Shotgun in hand:
 

I’m very impressed, a brand new one wouldn’t lock up any tighter. A deal of a lifetime. The engraving is crazy good. I’m looking forward to the letter.

Photos can be funny. The first ones you posted dont show as much color on the bottom of the gun. And these show a ton a beautiful colors. Like you said, photo forensics. You can only go on what you see at the time.

The first photos were from the auction house.

Top view:
 

How can I top this one? Never say never.