First things, for a $20,000 gun he takes lousy photos.
I would expect more effort from someone trying to sell something in that price range - or any price range for that matter, especially with today's easy to use digital cameras.

1. I'd like to see the proof marks on that gun before you do anything.

I just have a sneaking suspicion it may be a Black Powder gun or Nitro for Black powder gun that has been re proofed for 500 Nitro.

Weight 9.25 is light for a 500 Nitro and from that era,
very light. I have had 3 of them and none of them were anywhere near that weight, more like 11 lbs or more.

The stock is also way to light for a 500 Nitro,
my 3 x 500 Nitro's have stocks built like brick
shit houses, thick in the wrist and in the butts.
Again, looks like a BP gun to me.

So that is my initial observation. I may be wrong on
my assumption but the US is notorious for re chambering and / or re proofing guns so they are more "sellable" due to the calibre etc.

You said you didn't know what to look for in English guns so I am being overly cautious in highlighting possible issues to look for.

Finally, the guys descriptions of both guns leaves a fair bit to be desired. I would expect more from someone trying to sell guns at that level, plus the fact he dropped $7,000 off the first gun, to me that says he was hoping some dope would walk in and buy it at that price.

And then when you came along, he thought here is an opportunity to move it on at cost so gave a big discount.

Just my HO, I would be interested in anyone else's thoughts
re any of what I have written above.