Read the FAQs some more and visit wintersown.org. The seeds don't read seed packets and germinate when ma nature says to do so. Try some perennials and natives as well.

we will coach you.

I think it will totally depend on your weather after they sprout as to when to take the plastic off. Is there good ventilation? If there is then you can probably leave it on a little bit longer. I have never sown like that so I'm not quite sure. Hopefully someone else will have a better idea.

Hogan, from your username I'm gonna surmise that you live in New Jersey. What is your zone, maybe zone 7 becoz your state is coastal. If so then leave the saran on until you see the sprouts and as per the FAQs you can enlarge the openings in the wrap as the weather warms. In winter sowing the whole idea is to imitate what happens in nature, so even cold snaps are really ok. Find out when your average last frost date is and you can plant out around that time. Here in my part of Mississippi, it is April 15. The way you are doing it to plant right in a window box, I think is brilliant. it is just like winter sowing in a container, but you won't have to transplant the seedlings, altho very often you have to thin them out becoz there are just too many seedlings too crowded. You can pull them up (the ones you want to eliminate) or cut them off with a little scissors. Hope this helps.
Laurie