With hunting I mean the continuous CW and CCW short movements of the axis so it does not stand still, it keeps moving.
It is often used in servo applications where there is an encoder feedback path that is used as the current position which is compared to the desired position. If those two can not exactly be matched due to the resolution of the servomotor it keeps doing that same thing.
What is driving the stepperdriver, if it is a microcontroller then what I understand of your description you do not really need a motor driver ic. You can do the logic in your microcontroller and drive an H bridge.
I would forget about the A4988 unless someone else has a clever idea of using it.
If you need repeatability (step) and current protection have a look at the TI DRV8xxx series.