This collection of STUDENTS' SONGS (13th edition, ed. W.H. Hills, 1887) has a parody version of RIO GRANDE. It is by Hills and copyrighted 1881. Just goes to show how well known the chanty must have been by then.

http://books.google.com/books?id=U68QAAAAYAAJ&pg=PA34&dq=%22heave+away%22&lr=&as