Unfortunately, I have no floor head register, but wall mounted forced air ducts. I am going to be stingy about using my heating pads next year. As soon as I see sprouts, I'm either going to turn down or turn off the heating pads. It never gets that cold in my crawl space.
I use two shop lites each with a regular florescent and a grow light, to give the most broad spectrum of light.
Now there I have no problem. You should carefully pry up the plants trying to retain as much original growing media, as possible. Plant your spindly seedlings deep, as they will generate new roots. Not sure exactly what is your problem with transplanting?
Sherwin