Hi Dave
with the power reversed I'd expect a large fault current to flow through the diodes inside of the 8 FET's that make up the 2 H bridges
that control the power to the stepper motor coils
the FET's may be hidden between the PCB and the heat sink
if your very lucky that's all you need to change but its possible the overload to the current sense resistors may of damaged the resistors and possibly
the circuit used to measure the motor current
can you post pictures of both sides of the PCB?
John
PS
the diagram of the A4988 IC's internal circuit shows the usual H bridge and current sense resistors
that will be built out of discrete components in your KL8056d
Attachment 262634