Great stuff. What made me curious about the version I heard last night (basically this one) was the last line of the chorus -
"At the bottom of the belly lies the cuckoo's nest."
Spelling it out like that seemed very unlike a real bawdy ballad - once they've set up a conceit like that they usually keep it going more or less forever. And it turns out that the chorus (which was originally the last verse) has been jazzed up - from

But give me a girl with a wriggle and a twist:
That is pleasant and good-temper'd with a cuckoo's nest

to

But give me a girl that will wriggle and will twist:
At the bottom of the belly lies the cuckoo's nest.

Now, who's Oscar Brand?