What you need to do is be part of one of the large corporations who has a bulk ticketing deal with BA (or VS or AA etc). Each deal is worth many millions and receives extremely good support from a dedicated account management team. If you are a senior executive in one of these companies, you will also personally receive the highest level of membership to the executive club and your own, personal account manager. I know this, because I used to be in such a lucky position.
I'm not any more so if I have a problem, like you and about 55% of the rest of the travelling public, I'm ******.
That's the way it is...