The Traditional Ballad Index takes "The Drowsy Sleeper" back to 1855 (noted previously) but the version found at the Bodeleian by Toadfrog puts the date back to 1817. These broadsides were mostly cheap printings of still older songs. I have looked under "Silver Dagger," "Go From My Window, "(Fond) Affection," "Broken Heart," and "Sorrow" but found nothing that fits.
This version has "Jemmy" going to sea and the maid apparently sets out to starve herself. The brides portion of 5000 pounds does not seem to appear in the American versions.
Because this seems to be the earliest, and because of its difference from others, I am adding the full text.

Lyr. Add: THE DROWSY SLEEPER (1817)

Awake, awake, ye drowsy sleeper,
Awake, awake, 'tis almost day,
How can you sleep my charming creature
Since you have stole my heart away.

Begone, begone, you will wake my mother,
My father he will quickly hear.
Begone, begone and court some other,
But whisper softly in my ear.

Her father, hearing the Lovers talking,
Nimbly jumped out of bed,
He put his head out of the window,
But this young man quickly fled.

Turn back, turn back, don't be called a rover,
Jemmy turn back and sit you by my side.
You may stay while his passions over,
Jemmy I will be your lovely bride.

O daughter, daughter, I will confine you,
Jemmy he shall go to sea,
And you may write your truelove a letter,
And he may read it when far away.

O father, pay me down my portion,
Which is five thousand pounds you know,
And I'll cross the wide watery ocean
Where all the hills are covered with snow.

No, I will not pay down your portion,
Which is five thousand pounds I know,
Nor you shant cross the wide watry ocean,
Where the hills are covered with snow.

O daughter, daughter I will confine you,
And all within your private room,
And you shall live on bread and water,
Once a day and that at noon.

No, I will have none of your bread and water,
Nor nothing else that you have,
If I can't have my heart's desire,
Single i will go to my grave.

Crome printer (Sheffield- in ink)
Harding B 28 (233) Bodleian Library

Quite a variance from "East Virginia." Most song compilations separate "Silver Dagger,' "Drowsy Sleeper," Fond Affection," etc., although there are parallels and wandering verses. The simplicity of "East Virginia," to me, suggests that it may have originated independently. I guess that this can be argued indefinitely.