So, with a full flight, that probably means it's coming up relatively soon, and that most of the other passengers know the flight is full. I'm sure a lot of people have already added EBCI, since many people do it at the time of booking. My understanding is that the earlier you add EBCI, the lower your number is, so to add at this point, you'll probably get a number somewhere in the Bs. Since you're traveling with a 1-year-old, your family boarding status will get you on the plane earlier than an EBCI would.