I'm wondering if this is the best name for the song, since it seems to be based on what is apparently a floating chorus.

Here's a version of a song with the same chorus from the Bodleian site, dated between 1684 and 1686.

I've translated it below.

GRIST GROUND AT LAST
or
THE FROLICK IN THE MILL
Printed for J Clark, W Thackeray and T Passinger

Millers that grind each pretty lasses grist,
Consider now how many you have kist:
And see if any with kind Molly can
Compare: if not, pray all from hence begone.
Yet stay and hear the song, 'tis rare and new;
And millers know such things are often true.
Tune of, Give ear a while, &c. or Winchester Wedding.

Give ear a while to my ditty,
All you that intend to be merry
I'll sing you a song that's witty,
Of which you will never be weary.
The matter I plain must tell ye,
Is of a conceit refined,
The pretty device of Molly,
Who has too often been kind:
Says old Symon the King,
Says old Symon the King,
With a threadbare cloak and a mamsy nose
Sing hey ding, ding, a ding, ding.

She went to the mill with her grist,
To see it most neatly ground,
But found the miller i' th' mill,
For his stones they would not go round.
He tryed and he tryed again,
But he could not make them obey;
His labour he lost in vain,
And could not tell what to say:

She takes the matter in hand
As loath of any delay,
Whilst the miller amazed did stand,
She thus unto him did say:
Come hoist up the canvas with speed,
And I'll make the stones go round;
The cogs from cobwebs once freed,
My grist will quickly be ground:

When strait the sails were drawn up,
Exposed to the weather and wind;
When as the miller a top,
The weather bein right did find,
Yet found the motion but small,
Which made him begin to misdoubt;
That he would do nothing at all,
For Molly began to pout:

But urging her grist to be ground,
The fault she long searched to know,
And the wise of the mill she found,
For why? the stones were too low;
Then gently she moved the beam,
And setl'd them in their place,
When round the sails did skim,
And her grist was ground apace:

More sacks on the mill was the cry,
Let's now work and save the wind;
But at last the miller lay by,
He had no more grist to grind:
But glad was to find one so witty
To help him out at a dead lift,
Swearing that none so merry
had e're set his mill adrift:

Her grist she had tole-free away,
& might have the like when she pleas'd
For the miller he ne'er said her nay,
Once his labour was mightily eas'd:
The lasses that came to the mill,
They envied our Molly 'tis true;
But let them lay all what they will,
Molly's the best of the crew:

F I N I S