Phil, you say
Similarly, the song he called "Reynardine" in the revival arena is given its standard title "Rinordine" in Folk Song in England.

Have you looked in the Bodleian Ballad library? You can find it there under all sorts of strange names, but it is usually called The Mountains High. In this version, his name is Rynadine, which isn't far from Reynardine.

The mountains high