What kind of detailed records do you expect to find? If they were Yankees we don't even have a complete set of names as to who served. Don't think you will have when they enlisted etc.and what color eyes they had. Things did not work that way. I do not think they were paid on a regular basis. That is the only time there was an accounting. The Loyalists records are not much better. You should feel lucky to find the names in muster roles.
You need to go to Canada. It is not far if you use the internet. In the state the DAR and the SAR are big but up there it is the UELs. They are much more web freindly than their US counterparts.
Use Google. Try Delancey not Delancy. Both are proper in the 1700s but the first will serve you better.
That is the same with Westchester Refugees the were the Westchester Chaussers. Not that anyone used that name in the 1770s but they do now.
If the Loyalists don't have much you can try the McDonald papers. That would be a great deal of work to go through that stuff.