Well, multiplexing by moving the ground around was a fail.
The idea was to use two to four digital pins and change which was tied to ground and which was floating.
So tie a pin to ground, measure all analogs, tie a different pin to ground, measure all analogs.
Basically two rows of sensors, and which digital pin was tied low would determine which row I was reading.
Moving the ground around didn't work. At all.
Flipping the polarity of the entire setup so I was setting the digital pins HIGH and then using INPUT_PULLDOWN worked, but then I lost 2/3 of my range. This may seem backwards, but remember I'm reading the charge accumulation so my reference is to the rail it's starting from.
I'm thinking this is due to the internal structure of the digital pins. Perhaps a small cap would give me the coupling I need, but then switching them would be a lot slower too.
For now I'm dropping back to 16 inputs. Maybe 20 if I can mount the 4 resistors I would need directly to the Teensy. I could use the other 16 digital inputs too, but I won't be getting to the 24 analog inputs I needed to do a full 12 key keyboard with 2 axis of control per key simply. Drat.