Sabine Baring Gould (Songs of the West, revised edition, 1905) gives substantially the same information, adding that The Choice of Inventions was directed to be sung to the tune of Rock the Cradle, Sweet John, which is to be found in Chappell's Ballad Literature and Popular Music of the Olden Time.  The set he prints, which was noted from "Old Capul", Nankivel, Merivale Bridge, around 1890, is substantially the same as Three Jolly Sportsmen, above.

He also refers to an (arguably related) song, Six Jovial Welshmen (in fact, he mistakes the title), which was noted by W.P. Merrick from Henry Hills of Lodsworth in Sussex, (June 1900) and appeared in volume I of The Journal of the Folk Song Society (issue no. 5, 1904):

SIX JOYFUL WELCHMEN

(Noted by W.P. Merrick from Henry Hills of Lodsworth in Sussex; June 1900)

It's of six joyful Welchmen,
Six joyful men were they,
And they would all a-hunting ride
Upon St. David's day.
Then fill each glass and let it pass,
No sign of care betray,
We will drink and sing, "Long live the King!"
Upon St. David's Day.
Then fill each glass and let it pass,
No sign of care betray,
We will drink and sing, "Long live the King!"
Upon St. David's Day.

When Crook-back'd Richard wore the crown,
As regent of the land,
No policy could pull him down,
Nor his proud foe* withstand.
A tribute he from them did seek,
Which they refused to pay,
And in their cap they wore a leek
Upon St. David's Day.
Then fill each glass and let it pass,
No sign of care betray,
We will drink and sing, "Long live the King!"
Upon St. David's Day.

*Merrick glosses this as Law.

This is the song that Martin Carthy has mixed with a "misunderstandings" variant (see Gary Gillard's link above), though Long live the King has been changed to while the bells do ring.  The melody as written down was without barring; J.A. Fuller Maitland gave a notional re-barring, with some note values modified, to approximate a likely rhythm.  A midi of his modification of the tune will appear at  The Mudcat Midi Pages  in due course, but can meanwhile be heard via the  South Riding Folk Network  site:

Click to play Six Joyful Welchmen.

The text printed in Alfred Williams' Folk Songs of the Upper Thames (1923), referred to by the Opies, is another Bold Reynolds foxhunt set, and was collated from around five variants.