This has been a fascinating read. We sang this song in grade school in the early 1960s as a repeating song (a la "99 bottles of beer on the wall"). It went like this:

10 little children lying in bed
9 were sick and the other was dead
Went to the doctor, doctor said
Better feed your children on shortnin' bread

Mama's little children love shortnin', shortnin',
Mama'sittle children love shortnin' bread

9 little children lying in bed
8 were sick and the other was dead
Went to the doctor, doctor said
Better feed your children on shortnin' bread

I can't remember what happens when there's only one left. I'm sure I got bored (or told to shut up) before I ever got to one.