God advice all around! Applestar, I don't so much have a self watering system as just watering from the bottom to control damping off, which my herbs tend to do if i water the seedlings from the top. (I try to keep at least as many basil plants as tomatoes, they're bff in my garden.)
I am afraid to leave them soaking in "extra water" for the reasons you said. I lost all my tomatoes to a nasty mold the very first year I had my own garden from keeping the seedlings too wet and leaving the lid on. Since the tomatoes are coming up and the eggplant seem to poking through I expect everything else to be making an appearance in the few days too and think it will dry out from the lights with the lid off.
Marlingardener, thanks, I don't know why I didn't think of that! My mom is a 3-4 social skills teacher. The seeds I have are for this climate and will probably do better than the generic ones the big box store donated. Her class recently got grants for some excellent composters, so I think I will gift her my seedlings along with some of my established compost. It works sort of like a starter if you add it to a new pile, right?