No one quite covers the late 18thC, so you'll have to borrow from other ranges.
Brigade, new Minifigs from Caliver and Greek war of Independence from Steve Barber are all a little late but do the trick and then you have TAG and Old Glory as well, a little too early perhaps but do the same.
I wouldn't have too many jannisaries, and those that you field might be in campaign dress so a lot less formal looking than the blue and white capped ideal.
Good luck.