OK!
Hours of trial and error later some stuff has come together.
I closed the machine up, so I can't post any pics, but I'll try to describe the situation to the best of my abilities.
I found a resistor that has some good stuff on it. If you're looking at the component side of the board with the keys facing towards you it is the furthest right resistor, directly above the green strip of board that faces upside down. I think it is a 47k or 4.7k.
The top of that resistor makes a goodly amount of noise on several different spots, and I wound up throwing in some extra components there to tame stuff down a little. I wired the center leg of an NPN transistor (NTE 123 AP) to the top of the resistor and connected one of the outer legs of the transistor to the negative voltage on the speaker. On its own the bend doesn't do too much, but combined with some other bends it makes some great beats. The distortion changes a bunch depending on which of the four settings the keyboard's volume is on.
Coming from the same resistor I also connected a 100n capacitor to another resistor. The second resistor is the leftmost in the cluster of resistors located diagonally up to the left. The cap connects to the top of this resistor, and accents the cymbal resonance.
I don't readily recall exactly where the bend that I mentioned in the previous post is, but it happens at three or four locations, so it shouldn't be too hard to find. Poke around on the vertical resistors that are directly to the right of the line of ceramic caps near the center of the board and you'll find it pretty fast. It does bass and snare resonance, and combines with the two above mentioned bends to make some excellent beats.
Audio samples coming hopefully tomorrow.