W.W. Greener in "The Gun and Its Development" 1896 states on page 250 "The invention of Choke-boring has been claimed by many and is usually attributed to American gunsmiths. Mr J.W. Long in his book on "American Wildfowling" states ... the earliest person to whom I have been able to trace a knowledge of it being Jerimiah Smith, a gunsmith, of SouthField, R.I. who discovered is merits in 1827..."

I have deleted part of this passage decrease typing time.

Greener describes various claims of improving the shooting of shotguns in the 1780's but apparently none were what we would call choke boring today that actually worked. this on page 249-250.
One appears to be a foem of choke "recessed" choke but the writer refers only to using a file type tool to scratch the bore back from the muzzle. It is further pointed out that this simply increased powder and lead fouling.

Greener also shows "relief boring" as being tapered from both ends and describes it as being done by boring from each end with a straight bit.
He calls a "jug choke" a "recessed choke". The tool for doing this was patented by an American in 1872.
I can fine no mention of choke boring at all in "The Gun" by W. Greener 1835. Perhaps he simply did not mention it. It is available online from Google books BTW.
Below are pages 250 and 253 from "The Gun and Its Development) 1896
Dan