Re-potting would Def hurt a lot right now. Baby banana plants are Very sensitive. Btw, while seeds need temp variations, baby bananas can easily be shocked by it. For young bananas, best to keep light and temp conditions the same till they get bigger. Oh, and do be sure there's holes in the bottom & lower sides of the dixie cup. Good drainage is Def important for any banana plant.
I haven't worked with seeds much, myself, but I do know that the soil they're planted in should be Very Well draining. Once the seed germinates, it will become a corm which is sensitive to water. Btw, you can probably scrape the moss/fungus off the top. Some growers have reported that their seeds have taken as long as 6 months to germinate.
An important thing to remember is that banana plants are herbs and what we call banana fruit is actually a false berry (more closely related to a seedless watermelon). The underground corm (rhizome) can grow & spread without putting up stems or leaves so a lot of patience is needed... probably why I haven't tried seeds yet, not enough patience. The temps in your house sound great for starting seeds in a sunny window!
I see your general location's closer to Manitoba & Minnesota around Thunder Bay. I can easily believe it's zone 4 with all the global worming we been having! Although ya really can't tell here in Oklahoma. Fall started out kind of warm but now so much cold air has drifted in, we're freezing our b*lls off
! Btw, another thing ya might try is putting the seed cups near a heater during the day. Not too close, though, and you'd want to move them away from it at night (maybe on a tray). I have 2 Orinocos that I'm growing from corms and they're taking off like madcats by the heater, yay
!
Gotta stop, for now. Home-school and time for English comp. If ya have any more questions, just ask and I'll answer after school.