Amplify voltage controlled current source in a instrumentation amplifier
I'm not modeling any resistance to the body. I'm connecting the
  current source outputs directly to the instrumentation amplifier
  inputs.


That looks like the problem - you are trying to inject a mA into a giga ohm (the input impedance of the InAmp) and not surprisingly the current driver cannot force 1 mA into 1 Gohm. It would be able to if the power rails were +/- 1 million volts but they aren't and cannot be.

Try putting 100 ohm across the output of the two drivers. This then forces a voltage of 100 mV and, with a gain of ten you will get 1V out. Your expectations of 20V out are unreasonable given that the InAmp power rail is 12 volt.

One more thing - you will need a galvanic connection between the driver circuit 0 V and the InAmp 0 V. The human body (a real one) might facilitate this via other "connections" but for your simulation you'll need one.

Try 100 kohm.