Ladyada, firstly, much love from the east coast of Australia. Everyone I speak to at my university (in the engineering department anyway) absolutely loves your work.
Secondly, what kind of transfer speeds are you getting between the MMC and the STA013? From what I've read SPI will only allow speeds up to 400kb/s. Are you able to collect/buffer the data and feed it to the STA013 fast enough to decode high bitrate files (300kb/s)?
(Or are you in fact using a different protocol...SPI seems to be the only one I can find any information about without giving someone $1000)