I made several, unsuccessful, attempts to get in to the AAIB as a pilot investigator. I managed to wangle a visit to Farnborough to discuss a university project and put a massive amount of effort into completing the application form and generally networking my way in. To no avail alas.
When they advertise they are inundated with high quality applicants and I guess they can pretty much pick just the right employee. I did, however, get the feeling that it is a bit clubby. I was, discreetly, advised that having British Airways, Cathay Pacific or Red Arrows on your CV would do no harm.
That said, it's one of those very special aviation jobs where you can do some good whilst working with some very good eggs.
I have moved on in life but wish you a lot of luck in your application!