The one I learned from my sister (and she learned from girl scout camp) is almost exactly like yours (with the minor changes of "zipping up their -" instead of "pulling down their -", and without the "Dark, Dark, Dark -" line) but with one more verse: your last line becomes "I know I know" and the final verse is
I know I know my Ma
I know I know my Pa
I know I know my sister
With the forty-acre bra!
It then transitions into a version of "Bedbugs and Roaches", which I'm calling "Beetles and Mosquitoes" for the purposes of documentation.