Howdy
During the percussion era, most shotguns were muzzle loaders, just as rifles and pistols were.
The earliest breech loading shotguns were indeed English, but they were generally very expensive, beyond the means of most average shooters. The first affordable, breech loading shotgun made in this country were probably those made by the Parker Brothers of Meriden CT. Parkers started being made around 1866. They were much more affordable than the English shotguns of the time, and I suspect many of them made their way out west, being recognized as the practical, affordable guns that they were.
Barber & LeFever of Syracuse NY is generally credited with the first hammerless double around 1878. Unlike modern hammerless doubles this gun utilized external cocking levers. LeFevre formed his own company in 1880 and patented a modern style hammeless gun, that automatically cocked the internal hammers in 1883.
The Stoeger coach gun really is not a replica of anything, it is a modern hammerless SXS with short barrels.
Not that there's anything wrong with that.