Finally figured it out.
To make the service wrench icon go away, get in the car but do not turn it on. Press and hold the dash light brightness controller (as if you're resetting the Trip A/Trip B ODO to 0). While still holding the dash light brightness controller, hit the start button twice without your foot on the brake (do not start the car). Keep holding the brightness controller until the wrench icon starts flashing, then let go. At this point, repeat the Cyrillic alphabet backwards. The next step requires a chicken and a good knowledge of Santeria. Get a plastic drop sheet; it gets messy.
For the record, I had reset AND turned off all the service reminders via the so-called touch screen which did nothing to make the icon go away. You have to go through this obscure song and dance to get the icon to turn off. Left hand, meet right hand...