OK, I've found a reason for the water underneath the steering wheel and in both sides of the rear. I'm guessing that the heater core is leaking and the runoff is sliding down and back. I'm also guessing that the leak is below where the air ducts run to the front passenger since that one well is dry.

The FAQ claims that getting to the heater core will lead me to find new and interesting uses for my knowledge of profanity. Is it possible to access the core from beneath the windshield wipers? That panel appears to be held on with only two bolts. Or am I just thinking wishfully?