I just happened upon this discussion while searching for some genealogical information on Trubshaws.

One of my Victorian forebears, Susanna Trubshaw, did some research and published a book of family records. In it she talks about RICHARD TRUBSHAW, a Staffordshire stonemason and quarryowner (he's my 6x great-grandfather, incidentally) who lived 1689-1785, and of his reputation as a wrestler. Her own grandmother knew the first and last verses of the song. However Susanna's brother asked around when on a visit to Repton, and returned home with six verses about the match, which Susanna published in her book in 1876.

I can send these to you if you wish, or post them on this site if that would be of general interest. Basically it relates that Richard Trubshaw fought "Richard Allen Green" at Repton. Green's backer is mentioned as Sir Thomas Parkyns, who became anxious that he would lose his money! (So the match must have been before Parkyn's death.)

My version of the song has no reference to "Bunny" rules, so there must be verses I don't know of. However from your later research it looks as if that ties in well with Sir Thomas Parkyns.

A book I consulted on Victorian architects says:
"Like other members of his family, Trubshaw was a man of fine physique and great strength. His fame as a wrestler is celebrated in a contemporary ballad which relates how he defeated Richard Allen, or Green, of Hucknall, who had 'reign'd Champion of Nottinghamshire, and the Neighbouring Counties for twenty years at least', until he was thrown by Trubshaw in a wrestling-match at Repton."

I hope this is useful...