I finally got the voltage difference and current outputs working on the Due. Took a little tweaking, but I finally got the characteristic pinched curved which is associated with memristors. I also found the XY persistent display isn't great for showing this, but acceptable. The system is also fairly noisy so the sweep is pretty wide. But it's good enough for solderless breadboarding.
I'm using a simple voltage ramp up and down instead of a sine wave output since it's much simpler to write an up-down counter than a sine wave generator. It's roughly 1.3Hz. In the time-domain display below the green is the voltage difference and the yellow is the current. These are both DC shifted up in voltage since the Due can't output dual-voltage on its DAC. The trigger is pointing to roughly the zero line.
I'm not sure which direction I will go next. I'd like to clean up the XY output and perhaps do a good sine wave. And then use level-shift op-amp circuit to get a dual-voltage output. Of course, that's not a fun as actually trying to use the circuit as a memristor to build things, so maybe I'll looking into building a simple wired-AND or wired-OR style logic gate.