Your Simple Stepper Code works just dandy. AccelStepper is definitely supposed to work with Due, so this is quite curious. It's particularly weird because AccelStepper code does work when the physical connections I mentioned in my first post are made with the voltmeter. I looked through the AccelStepper library code and couldn't see any specific references to the pins I'm using.
The board is actually built for six A4988s. I'm probably going to obtain a new board and see if the issue is still present. I think it's the logical next step.
Thanks again for your help; enjoy your weekend.