I have a H&H 500 BPE 3 1/4" as well.
The number is 8343 built around 1885. It is regulated for the 5 drams load as per the engraving.
I am still working on the load. I have had trouble with the chambers as the cases stick in them (especially the left one). It is not a pitting issue, but It looks like the 19th century BPE brass was much thinner than the 500NE stuff that I have. Even unfired cases tend to be hard to extract. I guess I should turn the necks...
I got my brass from Huntington's. The bores are .510" so no surprise there. I am currently playing with the bullets.
BTW you'll need a large press to reload this round.
Good luck!
WC