Greetings my good cowboyjared -
your first question
"when the self contained shotgun cartridge came into major use"
is unfortunately too vague: "major use" is heavily dependant upon "who" and "where".
Those who lived in more remote frontier regions , being scantilly supplied, would have relied on ML not only due4 to the ability to tailor every load to the situation, but also because they could not afford to depend upon some one else for more cartridges to arrive at some unknown delivery time.
A rough idea of timeframes can be obtained by examining patent dates.
Whilst they were invented in 1833, "In General" pinfire shotshells were commercially available and in wide use amongst he well-to-due in Europe and the East Coast by the late ~ 1840's, when the pinfire cartridge was improved by Benjamin Houllier (Paris) . Their use declined after ~ 1860's when cetnerfire shells became prevelant. After that a variety of centfire shotshells were introduced, but pinfire shotguns continued to be produced and sold into the 1870's.
Needless to say, pinfires are not overly popular with CAS shooters.
Yoiur second question:
"why do current manufacturers make their double barrels based on the 1878."
I expect due to popularity and the small market. The 1878 is a reliable boxlock design, relatively easy to manufacture, and there is a limited market of those wishing to buy a hammered smoothbore.
Your best bet for alternatives is to search the aetherwaves , especially GunBroker, Guns America, etc...
yhs
prof marvel