Birmingham proved 1875 - 1887
Bore 16 would be .662" - .676" at 9" (fractions were not used until post-1887)
With those wall thickness numbers the .673" is likely original
Muzzle 18 .637" - .648"
.021" constriction would be .652". It's possible the chokes were opened slightly.

BTW the Bogardus Gun Club guns were introduced about 1874, for the U.S. market. I couldn't find how long they were offered.
https://www.doublegunshop.com/forums/ubbthreads.php?ubb=showflat&Number=662940 (Skip p. 2 wink )

January 3, 1878 Capt. A.H. Bogardus broke 5000 glass balls at 18 yard’s rise in 10 hours 40 minutes 35 seconds, missing 163, using a W&C Scott with 3 1/2 dram 1 1/4 oz. 8s.
https://books.google.com/books?id=DI4wAQAAMAAJ&pg=PA230&lpg

He did little competing after losing a 25-match series in 1883 to Dr. W.F. Carver “The Evil Spirit of the Plains”. They shot 100 targets each in 25 different cities, with Carver winning 19 matches, tieing three and losing three. Bogardus shot a hammerless Scott.

The last match I found was 1888 when he lost to Al. Bandle, of Cincinnati, on Christmas Day, 1888. Bandle killed 100 live birds straight to the Captain's 95. Both shot Smith guns.