I found the following plates on a French archive (http://gallica.bnf.fr/ark:/12148/btv1b84273032.r=Uniformes.langEN). I’m not sure who drew them and exactly when they were done, but they are clearly from the late 18th or early 19th Century. I have taken the plates depicting the units from Hesse-Cassel that served in the American Revolution and put them in one file.
Click on this link for the file in .pdf form: Hesse Cassel Uniforms 1776
Here is a sample of the plates (the Rall Grenadier Regiment):