The Age of Revolution in the Irish Song Tradition 1776-1815, edited by Terry Moylan, is published by Lilliput Press, priced £15.99.I bought this book on Martin's praise about it here, and each single word of praise is true.
However, the information you are looking for, Big Tim, is not in the book. There are about five songs about Henry Joy in the book. For the one that has the line you cite Moylan gives no author in the notes and a very similar song cites the same three names as possible authors as above.
Wolfgang