There are two copies of Menzies Rayner's Universalist Manual, or Book of Prayer on Ebay. Both the 1853 edition. Perhaps it wasn't as rare as its thin treatment or omission from the standard histories suggests.
Some quick Googling suggests that Menzies Rayner started out as an Episcopal priest -- certainly his prayerbook reflects this inheritance -- and he's likely had served St. John's, Elizabeth (then Elizabeth-town), New Jersey after 1795 to 1801. It still exists.