Sprouting seeds need to not dry out, but you don't want them floating in soup either. If it's hot, you may need to sprinkle a little multiple times to keep seedling moist.
Once they have true leaves and are putting out root systems it is important to not keep them so soggy. Let the top inch or so dry, but not the soil at the bottom (so, really, the roots are still not drying out, since they go all the way down) A good way to check if the soil is still moist at the bottom is to try lifting the pot. A dry pot will be much lighter than a damp one. Since you are using makeshift containers, did you remember to drill holes in the bottom? (I think so, since you have them sitting in trays
) Allowing extra moisture to escape makes getting the watering balance much easier.
Western exposures can be tricky. Plants aren't getting as much sun as they really like, but the sun they do get is hot and sudden and makes them wilt. Doesn't mean you can't grow anything, but if some things fail, it might not be something you can control. I still struggle with some of my western exposures.