I can understand people not wanting to give specific details but a date and flight number would be extremely useful. The BA Board is well known over many years for helping passengers who need guidance. Even though we bicker from time to time with varying views on matters, there is a huge amount of experience here and there is genuine goodwill trying to advise you.
It's not clear whether you have done so or not but if you raise a complaint with BA on ba.com then it will be given a case number and enquired into. I don't know the exact timescale of getting a reply so perhaps those in the know can advise on hat but 4-6 weeks is not unusual.
Did you get any form of reply from BA when you wrote your letters?
Here is the link.
Complaints and claims details