I just switched out the main board and the problem persisted, so I'm fairly sure it's not that. I'm gonna try the amplifier next.
UPDATE: it wasn't the amplifier either. I had pretty much much set the axis limits on Joints 4 and 6 to "none" and over the course of a few weeks' testing Joint 4's angular position got to over 8,000. I guess the system just *really* didn't like that, because I reset Joint 4 to its position within 360 and the problem went away. What a headache...