Problem solved.

Somehow, the pullups on portA have been enabled.
This forces current into the ADC pins along with the sensing input, and 
pushes them up near, and past, Aref.  When this happens, the ADC output 
drops to near zero.

I checked the LST file, and I don't see anywhere where those pullups get 
turned on, and I DO see an explicit turnoff in the init code, but disabling 
the pullups right before the ADC measurement solved the problem.

I'm not sure why they allow pullups when the ADC is enabled, but they do..
  

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