Still having trouble getting the Raspberry Pi to communicate with the Cape, but I have finally narrowed things down a bit.
I am using an Arduino Uno to debug the Cape's UART (running the Serial Monitor on the Arduino IDE). When I touch a jumper to the pin on the atmega328 chip itself, I get the proper readings that the cape should be sending over UART. However, when I connect to the pins (it's supposed to be either 24 or 26, but I tried just about 8 - 46 just in case) I get nothing. Additionally, tests with a voltmeter show that the atmega is putting out slightly under 5 volts, whereas none of the pins are putting out anything.
Looking at the cape schematic, there is a line under the voltage translator that says a pull-up resistor is required if either the atmega or BeagleBone are in hi-z mode. Is it possible that I just need a pull-up resistor?