First off, let me say I don't want to get into any heated discussions on this one
but the fancy fringed edged and 'caped' heavy linen hunting shirts used widely during the war of 1812, and probably used a fair bit in the AWI (though opinions among historians vary even on this) was almost certainly yet to be developed at the time of the FIW.
Hunting shirts were around in the FIW but appear to have been a very plain wrap around style worn over shirts and often waistcoats and under a waist belt, or simply the pull-over workman's smock.
I know that there are many about who adhere to the thought that the tufted-fringed caped hunting shirts appeared fully developed rather than evolving from simpler plainer garments, but most of the 'evidence' would seem to be taken from 19th century depictions. Attempts at reverse-engineering historical detail never really works for me, I prefer sound contemporary evidence where available.
I've seen some beautifully painted AWI figures in hunting shirts painted as part of an FIW army, but they still look very AWI.
I would say though, if it pleases you to use them in that way, what the heck, use them.
Your mention of brown coated provincials would be my choice - how about one of the NY units in "drab"? Alternatively, as several of the colonies never actually got their troops into uniform, why not go for using militia as provincials, painting them in a mix of assorted colours but with quite a lot of brown, either as a scattering of uniform items or just a linking colour, after all: "The Yankees do so love a brown coat" is a contemporary quote.
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