I have some thing similar in one or two of my containers, but they don't have sprouts yet. The white fungus is on/in the soil. Mine are also draining well, I think.

Perhaps we should open them up to more air?

I had that with some indoor seedlings I added more air and used chamomile tea to water with (diluted). it killed the fungus right away. I think air may help you but I am a WS newbie.
Karen

This happened to me last year in a few lasagna tins. I did not have enough soil. People here told me to poke some more holes in the sides - the soil was staying to wet. Even w/ the white most of them germ. & grew.

Good luck Annette

Thanks, that gives me some hope. Last night the temp dropped to the mid 30's, so I'm hoping that did the fungus in. I also poked some more holes in the top. I'll keep a close eye on my other containers.