Hi Kate!
Don't panic.

Early Feb is a slower time of year so you don't need ADRs at every single place you eat. I went in early May as well as mid September and never needed to make ADRs except for the high demand restaurants. Here are some of them
Cinderellas Royal Table
California Grill
Victoria and Alberts
Chef Mickeys
Brown Derby
Le Cellier
Chef Mickeys sounds great. Taking the monorail to the TTC and then to Epcot shouldn't be any problem at all (15 minutes) and then you can do lunch whenever and wherever you like (besides Le Cellier). Disney will move your Coral Reef ADR a little later or earlier with a simple phone call provided they aren't too crowded (which they shouldn't be in early Feb.).
I don't know how long the BBB takes but i wonder if you're taking on too much there. Spending a day at MK, doing the BBB and hopping to Epcot for dinner may drain your little one. You may want to consider taking a break during the day at some point. It takes 10 minutes to return to your room at the Poly. Again it's a slow time of year and after 6 hours at the park you will have seen and done a lot. Maybe you could go to the BBB in the late morning? Rest from 1-3 and head to Epcot?
Regarding your extra magic hours, know that the Unoffical guide reccomends avoiding those since the crowds are heavier at those parks. You could watch Illuminations at Epcot instead! Pace yourself if you can. I know it seems like you won't have enough time to fit everything in, but I promise you the days are LONG at Disney.
Resting and pacing yourself will keep you and your little one much happier!