Okay, so I've solved one problem and come up with another. In order to get composite video from the little A/V board to the mainboard, you have to solder a wire to a spot on the bottom of the A/V board. Basically, you figure out which one is Composite from here
you also splice in a wire to Composite In, with an on/off switch between them. Now you can switch to composite video whenever you like. The C Sync line has nothing to do with it.
Of course, if you're not using the A/V board, then you just need to connect composite from the system to composite on the screen. That's it.
The new problem I spoke of earlier, is that when composite takes over, I'm not getting any audio. If I switch back over to RGB, I hear it. Switch back to composite, no audio. Why this is, I can't figure out. Doesn't RGB use the same audio lines as composite? Why should there be any issues? Argh.
Edit: Wait a minute. In the picture above (the modified one from the screen sticky), it shows two Right Audio Ins and two Left Audio Ins. Perhaps one is for RGB, the other is for Composite. I wonder what would happen if I just connected each of the Rights together and each of the Lefts together. Hmm.
Edit2: It works! Woo!