Congratulations on your work.
I don't think there is any doubt that the barrels are genuine damascus.
The style of damascus, engraving and style of action point to Belgian origin albeit proofed in Birmingham after 1904.
The very few pins in the lock plates also indicate a very simple lock design.
Re-browning is a matter of taste, personally I would but then I re-brown pretty much everything! It is what I do!
Black is an American aberration, keep to brown if staying true to British tradition. But in the end it is down to taste.
