I have always had pretty good luck calling back repeatedly, especially if I call the week before my trip. I got just about everything else I wanted last night, we leave this weekend, except for Crystal Palace. However, as people move things around at the last minute, it gets easier.
Also, out of all the places we have walked up to on a busy day, Crystal Palace has by far been the easiest. It is so large and people cycle through so quickly, that it is pretty easy to just walk up and eat.