Jim--since going all modern with this computer I have found my first written version of T.D.R.W. This consists of three verses and a chorus from a 1914 American publication called "The Live Wire-Collection of Prohibation Songs" there the tune is said to have been written by J.P.Crawford. No mention is made of who wrote the words.
Forbye the article mentioned in a local newspaper [and it may have been The Ayrshire Post] I have seen it given as composed by Hamilton Nimmo.
The music is given in the publication. If you are a reader you may be kind enough to let me know how it compares with the tunes mentioned by you.
Joe.