boylesg:
But with the 2 bipolar steppers I have played around with so far, both seem to prefer different pulse widths even with the A4988 driver.
I think you must be referring to the interval between steps rather than the pulse width. An A4988 is happy with a pulse width as low as 1 microsec.
The interval between steps determines the speed of a stepper motor. If you want a motor to operate at higher speeds you will almost certainly need to accelerate it from a lower starting speed.
I figured out what was wrong. I had the sleep and reset pins low. When I fixed that the NEMA pulse width I had been using with the Nema13s worked with this stepper. So it must also be a Nema or else a close Chinese clone of one.