Someone replaced the wood on that gun at some point. In case you were not aware.

Good to know, thanks! Stock, forearm, or both?

Here are some pics of number 2, which I believe is a VH 12 ga with ejectors.

Parker #2 - Serial Number 102341 (1901)
12 Gauge sxs with minimal engravings, 12 ga, Vulcan Steel barrels

Both.

Also, I believe I see a damascus pattern partially obscured on the barrel flats. Does the top rib say "Parker Special Steel" or "Damascus Steel"?

There is also clearly visible on the barrel flats (of the Grade 2 20 gauge):

4
D

Making a picture of the rib marking more interesting.

A couple more shots of the GHE 20ga

The barrels have been sleeved. They were damascus. Now fluid steel, done with monoblocking.
The rib mark has been changed. You can see the sleeve joints in the barrels.

oh well, all is not lost, as they say. Sure the stock is not original and the damascus barrels have been mono blocked to fluid steel. People did things to their guns without worry about their future value, but to make them more usable for themselves at the time. It would still be a sweet little 20 shooter. You have no money involved, and it was your fathers. Keep it, shoot it, have fun and enjoy it.

Thanks for the info, all.

The GHE 20 has always been a shooter -- my great grandfather and grandfather used it in the field regularly -- and my Dad shot numerous straights on the skeet field with it in the 80s. Not surprised one of them had the wood and barrels redone - it has been well loved and used over the years.

The VHE 12 was added to the collection in the 90s - have shot it a couple times, but it's been awhile.