I did not say "cheap" but I know a lot of reenactors who spend lot's more on lots of other stuff...
You don't have to get a Martin. I have picked up several 19th century no-name parlor guitars for under $200 dollars (uncluding refit parts- bridges and the like) that I don't mind taking out. And numerous fiddles, bows, and even coffin cases for the same. These can be made period in apearance to pass all but the apraiser's eye. Certainly as "authentic" as your Armi-sport Enfield.
I don't think that George W's servicable repro banjo's are outrageous at under $500.
Is it not unreasonable to suggest that people try it? At least players can go nylon and quit the flatpicking. T'would be an improvement, don't you agree?
What do you need? Maybe I can find stuff for you.