Mamet seems to have not been referencing a song itself so much as an aphorism derived from its presentation on items of crockery.
He relates the origin of the play's title in the Chicago Tribune in 1989
Finally, on a hunting trip in East Texas, Mamet got the title for his play. ''We were at a forge, watching a friend of mine pound out the steel for a hunting knife, and I remembered the saying that you see on a lot of old plates and mugs:
Industry produceth wealth. God speed the plow.
''This, I knew, was a play about work and about the end of the world, so
Speed-the-Plow was perfect, because, not only did it mean work, it also suggested having to plow under and start over again.''
As you observe, Speed the Plow/Plough' is a Traditional song. There are (at least) two songs which use the phrase 'God speed the plough'.
One is an early 16th-century poem which borrows heavily from Geoffrey Chaucer's Monk's Tale and is described in Wikipedia as
a short, satirical complaint, listing the various indolent members of the clergy who will demand a share of the ploughman's harvest, rendering his work futile.
"The kyngis purviours also they come,
To have whete and otys at the kyngis nede;
And over that befe and mutton,
And butter and pulleyn, so God me spede!
And to the kyngis courte we moste it lede,
And our payment shal be a styk of a bough;
And yet we moste speke faire for drede. 1
'I praye to God, spede wele the plough.'
The other, which seems more relevant to the Mamot source is an early 19th century song which is known under various titles: The Farmer's Toast, Success to the Farmer, Jolly Farmer, and God Speed the Plough. This song, unlike the earlier, is not a complaint at those claiming a share of farmers' profits, though it recognises the reliance of others on the farmers' work, the whole is more of a statement of content with the speakers lot:
Were it not for my seeding you'd have but poor feeding
I'm sure you would all starve without me
But I am content when I paid my rent
And I'm happy when friends are about me.
The full phrase Mamot quotes doesn't appear in the song, but as this image of an antique cider tankard shows, when part of the song was reproduced on plates and mugs, a line about industry might be added as a sort of caption, which suggests that it is items bearing this later verse that Mamot was referencing.