Well, I finally got it working.
I ended up imaging Ubuntu 14.04.2 onto the internal memory of my BBB. After updating Ubuntu, I followed the instructions at https://github.com/adafruit/adafruit-beaglebone-io-python to ensure that was setup… I don’t know if that step was important before installing the Unified firmware at https://github.com/OpenSprinkler/OpenSprinklerGen2 . At least it works now. Because I did not use the normal Opensprinkler image, I unfortunately do not have the “demos” folder… I’m not sure if I really need it though.