How can I maximize the source impedance of the Arduino Due's ADC?
The maximum recommended source impedance for this MCU is 10K ohms. This takes into account sampling time and leakage of the I/O pins. However, you could easily add an op-amp voltage follower and get extremely high input resistance. 

The one I linked has typical 1pA maximum 30pA leakage over temperature and reasonable 3mV offset voltage, but may others are available. That particular part would cause &lt;0.1% error over the entire temperature range with 300M\$\Omega\$ source resistance! (Typically at room temperature 5G\$\Omega\$ for 0.1% error).