>> I've tried using a translucent "sterlite" type storage box (holes in the bottom and in the lid) to hold a bunch of pots with winter sown seeds, but that just doesn't seem to work very well for me, and I don't know why.
I cut the blue opaque lid of one of those down to just a "frame" or "rim" and used it to clamp down some poly film with slits cut in it. I only tried WS once, and had 0% germination ... except for some very slow Penstemon that took MONTHS ... but then germinated around 100% (????) Unfortunately, after germination, they took more months to grow bigger than 3/4", so for now I've given up on Penstemon and will come back to them when I'm not working 50+ hour weeks.
My "bad luck / good luck" with one try at WS doesn't mean anything. I'm still learning how to manage the long winter / spring months during which their temps would cycle wildly if exposed to sun, but nothing happens in the shade. And my first tub didn't have good venting for a while early on.
Fortunately, I like starting seeds indoors. I would do that exclusively if I had enough room. My current plan is to start seeds the way that works great for me (indoors) and then try to make room start more trays indoors by making a vented cold frame that (hopefully) will keep seedlings warm enough through the occasional cold night but not (hopefully) steam them to death on rare sunny days.