Can anyone recommend a ADC?

  1. Yes.
  2. Yes. Supply a steadier voltage to the strain gage. Can it run from 3.3V?
  3. Maybe not - the ADC has its own internal reference, if it's making say 2.5000 +/- 0.00005 from the 5V +/-5%, then its gonna show you the input varying from an input powered by 5V +/-5%.