This is absolutely fascinating, and I'm grateful to the unnamed guest for resurrecting the thread. I learned a somewhat different version of this song at a People's Music Network conference in 1988, sung (I think) by a union singer named Julie MacColl. The version I learned was:

Let the work I have done speak for me.
Let the work I have done speak for me.
And when I am gone someone else will carry on.
Let the work I have done speak for me.

I learned the whole song right there, zipper verses and all. I've sung it ever since, including at memorial services. I'd always wondered where it came from. It seems to be one of the few modern songs to have made it fully into the folk tradition.

Thank you again, Mudcat!

Dan