Hey SixMileHigh,
I'll have to keep an eye out for the pleated hair full make up on big issue seller at T4
I'd give BA a call on the 0870 60 80 747 number. I applied the second day of posting Cabin Crew back in Aug/Sep of last year, but didn't interview until February of this year!
Anyway, they called me up and offered me May or June. However due to my contract ending at my current airline, I subsequently called them back a few weeks later and explained to them I could start earlier, and when I called them up they took a message and got one of the 'cabin crew' recruitment people to call me back. They offered me an earlier date in April (which they just reconfirmed with me today, yay!).
I've found everyone to be supernice and helpful, so maybe if you give them a call and explain your situation...? I know that most of the people who actually answer the calls are in general recruitment, and so you may have to be a little bit persistent (in the nicest most friendly way of course!) to speak to someone dealing with Cabin Crew course dates specifically.
There are (apparently) still some spaces on the May and June LHR EF courses so you never know. Good luck!