Ok, we have a solution here.
I spoke to an electronics engineer at work, and he pointed me to the diode. Saundby, on his instructions page, says that he used an FD333 diode, but he says that a 1N4001 should work fine. So I used a 1N4001. As it turns out, these diodes are not interchangeable. The FD333 has a capacitance (yes, diodes have capacitance - I guess everything does) of 6pF. The 1N4001 has a capacitance of 15pF. My electronics friend explained it to me, something about the added capacitance causing the sync signal to overshoot. I hooked it up to an oscilloscope, and sure enough, the sync, which should ideally be a square wave, was spiking at its peak before settling back down. That was with the 1N4001. With the FD333, there is a smaller spike, and it settles more quickly. And the wiggle is gone from the picture.
Point being that you should use the FD333, and even though Saundby's page says that the FD333 isn't common (probably wasn't common back in the day), you can easily get it online now.