Wade,
I have hunted and shot competitively with a NWTG since the early 1980s. As was the case in the 18th and 19th centuries, this style of smoothbore is easy to build, is very versatile regarding loads and a hoot to shoot. A NWTG is the Model T of muzzleloaders. And if you've read any of my scribblings, you already know that "Old Turkey Feathers" is my go to firelock regardless of wild game or shooting game.
The bore diameter of existing original NWTGs varies by time period, by maker and by contract. My chart from Dixie Gun Works shows the standard English bore for a 16 ga to be .662.
So looking at Firearms of the Fur Trade by James A. Hanson & Dick Harmon, Encyclopedia of the Fur Trade, Vol. 1, Museum of the Fur Trade, Chadron NE, 2011 you will find:
Robert Wilson NWTG: 1751, 42-inch barrel bored .65 (page 146 & 147);
Robert Wilson: 1760 to 1770 era, 48-inch barrel bored .68 (154 & 155);
Benjamin Willets: Chief's grade, 1760 to 1770 era, 48-inch barrel bored .66 (182 & 183);
Thomas Barnett: 1820, 42-inch barrel bored .66 (178 & 179);
Thomas Barnett: 1805, 48-inch barrel bored .64 (170 & 171);
Robert Barnett: 1792, 34-inch cut down barrel bored .64 (168 & 169);
John Sharpe: 1818, 36-inch barrel bored .65 (174 & 175);
Richard Wilson: Chief's grade, 1750 - 1760, 44 1/2-inch barrel bored .70, John Kinzie, Chicago trader (181 & 182);
Henry Morris: Chief's grade, (attributed 1802 to 1813), 48-inch barrel bored .69, (186 & 187).
There are other research sources, but Hanson's Firearms of the Fur Trade gives a good cross section of bores, barrel length, makers and dates. There are also guns shown in the .60 to .62 range, but that is not what you want.
My advice is pick a time period, maker and either use an available barrel or have one made in 16 ga/.662. I doubt Thomas Barnett, Robert Barnett or John Sharpe would notice a thousandth or two variation in the bore diameter.
And regarding recoil, the versatility of a smoothbore allows for matching the tolerated recoil with the powder charge, ball or shot. A respectful and humane load is required for any game, and range time will determine what that load is.
As an aside, I have shot in competition with as little as 35 grains of 3Fg (.610, 344 gr. bare round ball with leaf wadding) and loaded Old Turkey Feathers (originally bored .620 and now mics .629 after 40-plus years of shooting) with balls ranging from .530 to .610 and shot from #9 to 00 buck. All of which knocked down steel clangers at 75-plus yards, busted clays or downed fowl or fur. As I have written for years, you can't beat a Northwest trade gun for versatility and FUN! Build the NWTG you want and you will not be sorry!
Be safe and may God bless you,
Dennis "Denny" Neely