All of the above versions seem to be American.
For a possibly earlier English chant obviously related.(1950s Yorkshire)

Once upon a time when pigs ate/shit lime
And monkeys chewed tobacco,
The little piggy run with his finger up his bum,
To see what was the matter.

I'm sure I've seen other British variants too.

Ah here we are.
Chambers Popular Rhymes of Scotland p57

Lang syne, when geese were swine,
And turkeys chewed tobacco,
And birds biggit their nests in auld men's beards
And mowdies del't potawtoes--

which kicks off a folk tale called The Wife and her Bush of Berries.

I have another half dozen versions from various parts of Britain.