Well, I'm fresh out of ideas at the moment. Since the noise goes away when you connect the probes together, that would indicate:
a) The noise isn't due to feedback loop instability
b) The noise isn't due to the selection of op-amps or resistor values
c) The noise is not otherwise contributed by the circuit or injected into the circuit.
This indicates that the noise must be contributed by the human's body, as a potential across his/her arms. This leaves two possibilities:
a) The human is picking up electromagnetic interference from the laptop or something
b) The noise is the result of other signals being carried through the human's body (brain waves, digestion, flexing muscles to impress girls, etc.)
I could be wrong, but it seems to me the only steps that can be taken would be:
a) Increase shielding to prevent EMI
b) Use multiple probes and find the covariance between their signals, to weed out other bioelectrical impulses
c) Use large probe pads to average out local bioelectrical impulses
I'm curious to find out what ends up working for you, so keep us posted.