I'm now in NYC, staying for two days to do research at the New York Public Library and the New York Historical Society.
The NYPL is one of the most amazing libraries in the world. Although the special collections/manuscript department has odd hours, and there is a long wait from the time you order material to receiving it, there are some real gems here. I found the book Nymphas to Sosipater, which was edited by John Erskine and contains published letters from Joseph Bellamy to Erskine that talk about the theology of Robert Sandeman. According to Worldcat, there are only two books extant.
Miscellaneous Personal Name File in the manuscript department. Take a look at the list of names and see if there is anyone of interest, and then order the particular file. The file may contain a scrap of paper or several personal letters, and so it is a bit of a treasure hunt. I have found some very interesting letters in the Miscalleous Name File.