Below are some additional lyrics I found in a blog.

I figure this would work as a second verse:

'Taint no use to try to slow me down.
Can't stay, just can't stay.
Had a man and had him throw me down.
He's gone far away.
It was solitude
That put me in this mood.

I'm not sure how to fit these words to the melody. Maybe they would work as replacements for "Made my will ... straw hat floats" in repetitions of the chorus:

Bring on your water cold and deep.
On your bosom let me sleep.

Nile or Danube, Amazon,
All your rivers, bring 'em on.

And David Deacon posted the following lines in another thread, and they haven't been reported elsewhere. He said he learned them from Lynn Hardy:

I can't swim, neither can I float.
I got a lot of lead pipe in my overcoat.