Just wanted a sanity check here, in case I missed out on anything, before I prepare to take this case further. Genuinely unhappy with the way this was handled.
I wish you luck but would rate your chances as less than 5%.
BA will say that the lack of crew for your flight was due to rostering issues caused by the weather - not unreasonable. If challenged on later flights leaving first they will say it was because they wanted to delay as few people as possible - again not unreasonable.
On the rebooking they will say that they expected a crew to become available and in any case there was not sufficient capacity on later flights to rebook everyone.
Unfortunately when weather is involved the airline holds all the aces.