How to interface with a bus that's powered when the rest of my circuit is off
Ok, I've solved this. I've added buffers between the control box and the drumpad controller. This is in addition to the buffers between the microcontroller and the drumpad controller. 

So, the buffer configuration on (one) of the lines would look like this, with other parts of the circuit omitted for demonstrational purposes. 



The unconnected pins on the buffers are the output enable pins, which I didn't connect (again, demonstrational purposes).

This circuit solves the problem because there is never power on the output of a buffer when the buffer isn't powered. Therefore, no reverse flow occurs.