One thing not fully covered in this lengthy thread is the relative success of family seating assignments.

I know this is a moot point for the OP as all's sorted. But the OP did mention his "two young daughters", by which I infer under 12 years old.

BA's family seating policy is this: If you don’t reserve your seats in advance, we’ll do our best to seat your family together a few days before your flight departs. However, the seat selection may be limited at that time and your seats may be split across different rows or the aisle. We will make sure each child under 12 years sits next to an adult from your booking but children over 12 years are booked as an adult in our system and may sit separately.

I'm interested to know - for no other reason than nosiness - whether this works well in reality and families do end up being seated together, more often than not.