All three songs probably came from the English broadsheets. They might have been carried to Oz early but I rather doubt that they entered the singing tradition until fairly recently. I will, of course defer to Bob Bolton, etc., on this point.
That English broadsheets of the 19th c. were carried abroad is shown by those found in the U. S. and Canada.

'Me' is sung by so many current American-Irish singers in the bars (pubs) that it 'grates' a bit, to use your words.

The 'll' in traveller is accepted by many North Americans, not as often as the single 'l', and it given without comment in Webster's Collegiate Dictionary, along with similar constructions (focused, focussed). Modern N. Am. writing drops the 'll' and I think now most children learn the single 'l' in school. I presume OZ remains closer to English 'll' usage.

I had another broadside version I was going to post for comparison; I should do it before I forget entirely.