Regarding Mr. Burns,
It is hard to tell, but it does look like post 1812 surplus (which doesnt help much.) After the War of 1812 there was a major overhaul of arms by the National govt and the states. What could be repaired and servicable were kept, others given to the states honoring the 1808 Militia Act requirements of arming the states. That resulted in giving the states junk the Feds did not want to keep, beginning in the early 1820s and were promptly refused. The rest were sold off by public auction. The states likewise sold off these worn and outdated arms. Those sales increased with the arrival of percussion arms. The 1840s was when many of these public auctions occured.
With that, Mr. Burns' musket could be "unofficial" Models 1808 or 1812, could be a Harpers Ferry arm due to the stock, or a contract. It could also be an 1816. The trigger guard doesnt help as it is too difficult to see the sling swivel location. If it had the stud typical of early '16s and the various 1795s, its not visible now. The hammer looks to be rounded and not flat like the 1795s, increasing the likelihood of a model 1816 in some form.
Im actually intrigued by his modification of cutting the forestock, yet, keeping the barrel length. Im not sure if the barrel retains the rear band or altered for a key... she seems a bit short.
Referring to the post regarding militia men walking off with an arm, that most certainly happened. Sheriffs were responsible for collecting militia fines and cooperated with various militia officers to collect these "public arms." Most returned in terrible state. Some states were quite loose with their militias and armaments, hence so many Rev War arms being issued down south during the Civil War. Augmented by donations and purchases of "civilian arms" which many were surplus. The Civil War was the last conflict where this reissuing of surplus was implimented in any real scale, and seen much more often in previous decades back to the colonial days. Dont forget the massive usage of fussils and fowlers pre Mexican American War, save for the Texans which used everything.
Interchangeable parts due to standardization with the industrial revolution, along with the capitalistic prosperity killed the muzzleloader. One of the reasons why the cheap Belgian shotgun won the west, and the desire for breachloading arms. Revolvers were expensive! Sure cheap surplus arms, esp. post civil war resulted in tons of muzzleloading shotguns, but no one can deny the zillions (almost literally) of small arm manufacturers appearing in the latter half of the 19th c., and none of them, save for Bannerman and Whitney, selling muzzleloaders, and those two selling under the quantity vs quality models.
In all state troops kept whatever they had begrudgingly until better breachloading rifles became the norm. Even then... I recall troops in Alaska still carried versions of the trapdoor during WW I. We essentially had no artillery during that conflict, using French 75s once we got there... we still had newer but obsolete 3.2 inch bag guns and vaunted 3 inch ordnance rifles!