Got around to fixing the distortion in the display. My hacky OR gate was at fault; the pulldown after the diodes was ~500Kohms, but there was a ton of capacitance in the input being driven (74LS244 @ 5V), so minor power fluctuations were screwing up the sync. Went to a 680ohm pulldown and now it's solid.
@phooky nice! I had an inkling it was some capacitance thing (it kinda looked like what a cap does to an oscilloscope). But troubleshooting something like that would cross my eyes.