Jerry:
Did the seller say why the rechambering was done? Was it because the chamber was badly pitted, or because he couldn't get brass for it? If the former, the correct solution would have been to sleeve the chamber. If the latter, he couldn't have made a worse choice.
Have you slugged the bore? If it was originally a 9.3, I wouldn't have thought the groove diameter would have been .375" - more like .364" - .367". Rechambered to a .375, I had assumed it was originally a .38-55, not a 9.3. I would suggest that you do nothing until you determine what groove diameter is.
This gun is 110 plus years old, and was originally chambered and proved for a black powder 9.3 - in other words maybe 25,000 PSI, tops. Max pressure for a .38-55 is 30,000 CUP, and .375 2 1/2" Flanged is 31,900 PSI. The .375 Magnum is 62,000 PSI. It's now a .375 Magnum without benefit of re-proof. It goes without saying that pulling the trigger on a factory round of the cartridge it's chambered for now would be nuts - and that's the point. Just because the seller is willing to do something irresponsible (sell a weapon that is clearly unsafe for the cartridge that he's modified it to take) doesn't make it worth $1,500. I'll put it this way - if this piece were mine, and I got tired of it, I see two options to get rid of it responsibly. Either correct the problem by sleeving the chamber to a suitable, safe caliber (more $), or render it inoperable and sell it as a wall-hanger. Could you figure out how to shoot it safely as is? Maybe, but even if you could, that doesn't change the status of what it is. I see this piece as a wall-hanger only, worth wall-hanger money, a far cry from $1,500.
As to the mono-metal bullet issue, I wouldn't fire them in any double rifle, or cape gun, that I cared about, let alone one of that age. Been there, done that.