Firearms manufacture during that time frame was a small-scale affair - with many, many early gunmakers providing the public its arms - Hawken was a small shop, and Enfields were English-built and not readily available until the Civil War - the bulk of production belonging to the Crown.
Figuring out which one provided the largest production and all that you're looking for may prove somewhat difficult.
Given that these forums are pretty devoted to Cowboy and Western Action Shooting, and not Civil War reenactment or the Fur Trade era, but the era of cartridge firearms - perhaps there's another venue available that I'm not aware of at the moment.
Production records of the pre-Civil War time frame are spotty, to say the least - and often non-existent, especially from the smaller manufacturers.
Maybe the best way to answer this is to look at who were the big suppliers at the beginning of the Civil War - Whitney, North, Colt, Sharps, Hall, Spencer, Amoskeag, and so on and so forth - and then backtrack their history.
Those were but a few importuning Uncle Sam for his business - in order to 'make' their business.
Even back then, a Government Contract built and saved many a manufacturer.
Good Luck.
Vaya,
Scouts Out!