BA On-Line Check-in is 24 hours before departure even for a return flight it's always 24 hours before departure.
On BA, depending what price you paid for your ticket you can select your seat in advance but check-in is always 24 hours before departure.
I was informed by BA that the cabin layout (number of Y/J seats) is calculated around 2 days before the flight but, can also be adjusted on the day of the flight. I guess if OLCI was open sooner than 24 hours they would end up moving people around as a result of changes to the seating configuration.
I have often viewed my booking online and seen that the number of Y/J available seats changes, sometimes daily. For example Club rows extended say from Row 5 to 8 or vice versa.
I dont know your destination but, maybe there is an internet cafe there where you could check-in online?
Regards,
G-BPED