Anyway, I prototyped this motor:
It is a 2 A motor rather than the .4 A motor I was using. I went to a Big Easy Stepper Board to handle the larger current requirement.
In 1/16 microstepping mode, the motor turns very slowly and very smoothly. It looks like I can hook up a push button, and get one single microstep with each button press. It doesn't miss steps. That's all I was after.
I guess I needed a more robust motor. At .4 A, I guess I cannot expect each individual microstep to be accurate.
I didn't know about A4988 controller boards until this thread. It seems like they do everything the Big Easy Stepper Driver does. They're cheap and I just ordered 5 of them.
I wonder why the Big Easy Stepper Board even exists.
Thanks for your help!
Mark