Toby, my apologies to all, if my earlier post was construed as the gun having been proofed under 1875 Rules, as that was not intended.

Anyway, to avoid the apples&oranges conundrum, the "facts" laid before us by OP :
1. chambers might be 2 3/4" (but could be 2 5/8 - 7/8" ?)
2. heavy gun
3. cylinder barrels (.727 "straight thru'")
4. presume to have been Proofed under 1868 Rules.

The likelihood is that it was built for use of "ball and shot"....and not as Trap/Wildfowl gun.

Of course this suggestion has the usual caveats that bores are "as original", etc, etc. Supporting this suggestion would be that many shotguns imported to N A were intended for use on larger game in addition to birds. Also that this contention is not being substantiated by citing of post 1880 trap shooting reports, the products of "gunmaking" firms not existing at the 1872 date relating to the gun's serial no. and so forth.

Toby, that was an interesting picture of Whitworth barrels. Would you happen to know in what year the gun trade started to use Sir Joseph's steel in barrel manufacture?