I don't see why it WOULDN'T work...like you say, the concept is the same. I would be concerned about headroom, so I might consider propping some 2L bottle halves in various places to keep the tarp up, and secure it down on the edges...still adding your vent-holes.

BUT...the other huge concern is still those weeds. Professional grow mix, or prepared seed mix won't likely produce as many weeds as you'll probably still get with your tarp setup because the weed seeds are already present.

I'm sure others will chime in.

Quilt mommy, I did the same thing! I put clear plastic to "kill the grass" where I wanted to plant tomatoes. Uhh...in spring, it doesn't kill the grass, it acts as a nice greenhouse!

Pitimpinai has done what you're planning, and I've done similar with big domes from trays. The ground won't warm up the way it does in the containers, but it gives us the other WS benefits. Just make sure the plastic stays off the ground, otherwise rain and wind can squish or hurt the seedlings.

I see what you mean about keeping the tarp from suffocating the emerging seedlings...I suppose one benefit that I quite enjoy from growing in the jugs is having the ability to see the seedlings and know where I planted them.