Well, finally got steady sampling and writing to the memory card using a timer, the event system, ADC interrupts, some buffers and bit banging SPI to the SD card. How did the data look? I should be slightly worried about my medical condition :)
Rest assured, I hooked up my oscilloscope on the amplifier exit and saw a perfectly normal heartbeat amid a dose of 50 Hz mains noise. There's nothing a little debugging won't fix.