After deciding that the diode distortion sounded bad, I poked around the Polysix schematic and found a bunch of LM13600 in there that were just begging to be overdriven. Perhaps that's the compression and grit that I'm looking for?
So, I gave it a try. You can see a demo of the results here:
I think that it's a pretty interesting sound. I don't want it active all of the time, but I think that it's a cool effect. Now I just need to figure out how to make it usable without requiring that clip leads hanging out of my synth!
Chip