Looks like you got me. I did read a different version back about 40 years ago, and recalled it, but it was inaccurate.
https://trishansoz.com/trishansoz/waltzing-matilda/waltz.html
Off topic, but...There’s another called “And the Band Played Waltzing Matilda”, a horrors-of-war song about the WWI Aussie assault on Gallipoli. I sang it at our local pub’s Irish session a while back.