Suggestions for an ultra-low leakage diode
Try a green LED. Big bandgap, low Is. 

Edit: I just tried one for the heck of it at room temperature. Forward current of a generic 0603 green LED is around 100pA +/-50% at 1V and around 2nA at +1.2V. 

Blowing controlled +180 degrees F (82 degrees C) hot air across it (no environmental chamber here to do a proper test) +0.3V conducts in the &lt;200pA region, so in G\$\Omega\$ territory. 

At least that seems promising to me for a quick test.