is there a particular uniform style that’ an obvious gaffe?
I bought Lurkio miniatures in ECW-style that were missing the later 17th century European 'cravat', aka Steinkirk, predecessor or the tie. Technically, for the wargame uniform police types, that would be a mistake. Unhistorical.
According to my Osprey book 'Colonial American Troops 1610-1774' the uniforms might have resembled to the European uniforms. However, we're talking about far away colonies. Unpractical helmets were possibly traded with the local indians, the book writes.
Pikes are used against massed cavalry formations, but the local militias were small and the horse was uncommon in North America until the 18th century. So I suppose that a 1650-1700 'North American cuirassier unit' or a North American pikemen unit' or an 'Indian cavalry charge' would be such a gaffe.
Colonial military actions were raids on trading posts or skirmishes between a mixture of overseas troops and locals. I quote Osprey:
"Following the capture of New Sweden, in 1655 the Dutch were at war with the Delaware Indians. In November 1656 "munitions of war for 150 men" were to be sent from Amsterdam to the South River of New Nether1ands" (the Delaware river). The letter is interesting in that it reveals changes in armament and equipment. For 75 men, there were 'muskets', assumed to be heavy matchlocks with forked rests - bandoliers, swords, and sword belts. Another 7S men were armed With "tirelocks or snaphance" muskets - flintlocks - with cartridge boxes, sabers and saber belts. Gone were the mall shirts, although buff leather coats may have been worn."
In other words, if I would collect, paint and wargame the colonial war in North America, like you, I would buy infantry with floppy hats, swords and muskets and paint them predominantly in buff and leather colours. Indeed, like cowboys in long trenchcoats. Not formal, with the European wigs and steinkirks.
I wargame LoA in 15mm because of the formations. For colonial wargaming, I would consider individual basing and 28mm. Maybe a skirmish ruleset, like Sharp Practice or Donnybrook.