The main difficulty is of course that in times of mass disruption like yesterday (and a few others), airlines (be it BA or any others) are first and foremost constrained by what is or not possible and what they do know or not. In that sense, I think that even with the best will in the world, the risk is that given the circumstances you are living with, there is a high risk that even the "best" options might be uncomfortable and distressing, because the airline may try to rebook you on the next equivalent flight but that may in turn be cancelled or delayed, etc. Cabins are often full in J too so it is also possible that on some occasions, the airline may propose you the next available flight but with a downgrade to W or Y.

However, airline employees are (and should be) aware of the special circumstances that people have to deal with and the best advice is probably to be straightforward about your priorities. For instance, if you would prefer to cancel the trip or rebook at a later date rather than wait with some uncertainty say so, if you would prefer a later flight in your originally booked cabin class than the first alternative with a potential downgrade say so, if you would prefer to wait a bit longer to stay in the terminal rather than need to go to a different one to catch a flight with another airline, say so, etc. Since you mention that you are travelling on a 2-4-1, this suggests that hopefully, there is someone else who can indeed have those discussions whilst you try and find the least uncomfortable places to wait and my sense is that those discussions will significantly lower the risk that you be offered solutions that you would like to absolutely avoid.