I guess I have a bit of a dilemma then, as I need both hardware serial, and software serial.
I need the hardware serial because the program will need to constantly communicate with a RaspberryPi (or other Linux machine) for instructions from a Python program. Basically Python is doing all the heavy lifting (calculations), pulling information from the web, and interpreting user input (PS3 Dual Shock Controller).
And I need the software serial -- well, mostly for debugging right now. It might be feasible for me to rewrite the Python module to receive status/debugging data from the Arduino as well and eliminate the need for this LCD.
From what you said though, the hardware Serial still interferes with two of the interrupts (on pins 0 and 1), but any clues as to why I don't observe any problems when only using Serial.print() commands, while simultaneously having the interrupt attached to a conflicting pin? Whereas software serial raises an issue?