Here's another thing to keep in mind: Bridging an amplifier increases the amount of distortion present in its output, because of tiny differences in the output stage of either channel of the amp (even within the same chassis). Distortion in the bass is less audible, so bridging is a better compromise for powering dedicated low-frequency speaker systems. However, amps are less stable in bridged mode than when driving separate loads from each channel, and can't deliver as much current into the load at high drive levels.
It sounds like the clear solution here is to run the amps in stereo.