Wow, I got this working a lot faster than I thought I would. It's nice to not have too many problems to fix once in a while when writing new code.
I was able to write 60,000 512-byte blocks in 1700 milliseconds.
That means I wrote 29.30 MiB in 1.7 seconds, for a rate of 17.233 MiB/s. That is just _barely_ fast enough to handle an 8-bit 15 MHz ADC. Since the one I want to use is 12 bits, I will need to use two SD cards in parallel. But I was expecting this which is why I purchased a second SD card at the same time I bought this first one! :)
I just hope this 17 MiB/s can be sustained over 30 minutes. I kinda doubt it can but who knows?