I am not a dealer, but as a collector (with a tip o' the hat to Norm Flayderman), here's what I've learned about prices and collectability. There are three factors affecting value: demand, rarity, and condition. Demand is a slippery thing and can be based upon such things as type/model, appearance and proven historical provenience, among other factors. Many times a seller will suggest that a gun could/possibly/might have/perhaps been used by someone or some unit at some place at some time; Custer-range trapdoor carbines, for example. Without proof, such claims while true, are essentially meaningless and do little more than to possibly coax a few more dollars from the buyer. It's like saying a certain Committee of Safety musket fired the first shot at Lexington or Concord. Rarity, as the name suggests, also depends upon many factors. In this case, Springfield manufactured about 15,000 Type III M1812s. In original flintlock condition, a M1812 musket in good, original condition can fetch about two grand, give or take. As an arsenal conversion, the price drops significantly to several hundred dollars. If it was a local gunsmith conversion or if the gun is missing parts, has been overly cleaned, been cut down or is in otherwise in poor condition, the price will drop even more.
The bottom line is that the musket is only worth what someone will pay and that value is based upon the above three factors.
I hope this helps put things into perspective.