Well, my wife promised me that if I fried my headunit, I could buy a new one. So I took a shot.

I don't think there was any ground problem. I just didn't wire the headphones up correctly. The wires are very small, and difficult to work with, and I became impatient.

At this point, I am definitely walking away from trying to solder wires onto those little pins. To those of you who can do it: Wow. That takes more concentration and focus and patience than I have.
If I do try to build this adapter in the near future, I'm going with the Mouser unit, and start splicing (think the wire tap-ins I used to splice into the power will work for the sound?):



Oh well. The in-line FM modulator I installed is leaps and bounds ahead of the wireless FM modulator, so at least the sound is better than it was . . . I can live with it.