MarkT:
Don't leave us in suspense! What was the problem?
Sorry for the delay in responding. The problem was this: I had observed that the left and right channel of the glasses appeared to flash in sync with each other. Therefore, I concluded that they probably shared a common driver, and so I bonded the tip and ring of the TRS jack together. There was little justification for this; I just hate to have copper in the cable that is going to waste, so I figured, why not use both lines to carry the signal instead of just one.
After hours of troubleshooting, I finally thought to pull out the junmper that was bonding the channels, and the problem immediately went away. Upon further investigation, it turns out that the left and right channels are actually distinct, and they are flashing slightly out of sync with each other. To the naked eye, it often appears as if they are flashing in sync, but they sometimes aren't. My best guess is that when the frequency of pulses got high enough, the fact that both left and right pulses were being combined causes the LEDs to see enough current to light up solid.