The aftertouch kicks in as soon as I press a key, any key. Changing the velocity curve setting has no effect. The only way I've found to disable it is in preset and sequencer mode, setting pressure to "none". I played the SD1 via MIDI from a controller and no aftertouch was triggered, so the problem is definately in the keybed's control circuitry.
At the suggestion of several independent acquaintences, including a former Ensoniq engineer, I'm going to replace the 68HC11A1P microcontroller on the keybed's control circuit board. It's an educated guess so we'll see what happens.
Thanks again for your thoughts.