Och, Artful, ye're oskin' the impossible, mon! Nevertheless, here is Lame Effort #1, which breaks several of your rules, if nothing else, above all the expectation that it would make any sort of sense. (It's more of a Songs of the Pogo type of effusion methinks.) It is based, of course, on Earl o' Murray, which you can easily go look up for the corresponding lines:

THE LAST LAY OF LADY MONDEGREEN

Ye high lambs, and ye low lambs,
O where are your beans,
Ye have chained the Earl Amurray
To Lady Mondegreen,
Away, Bazooky Hungrie,
Elsewhere for frigid tay,
A badger strung a widget,
And for badger, hymn the sleigh.

He was a flawed talent,
And he paid at the shove,
And the bony Earl Amurray
He was the Quince Zone love,
He was a flawed talent,
And he fought in the ring,
The bony Earl Amurray,
Too tight to be a king.

O-lan and his lady
Lock oar and fasten down
Ere three Earl Amurrays,
Astounding, view the clown.

Ye sly lambs, ye show lambs,
Oh what is your scene?
Ye have changed the early scurry
For Lady Mondegreen,
Away, Petunia Humpie,
Aware, foredoomed, ye stay,
A bad jar is the limit,
And a bad jar is her lay.