After a lot of hunting around, I finally found a great resource on using Arduino as a SPI slave: http://www.gammon.com.au/forum/?id=10892
Plenty of resources exist for using Arduino as a SPI master (including Arduino’s own SPI library), but I couldn’t find much on using it as a slave. That link includes information on both. I hope someone else finds it as useful as I did.
To assist in debugging SPI (master or slave) with Arduino (or any other microcontroller for that matter), I suggest using a logic analyzer such as this 8 channel Saleae USB Logic Analyzer:
(image property of Amazon)