Need to convert small stepper to larger motor

I have a machine that uses a small 4 wire stepper motor for a feed
mechanism. The controller is a surface mount electronic black box that
houses a lot of other electronics and has no apparent stepper driver
and no standard step/direction signals. The motor only spins in one
direction. I need to replace the motor with a larger one and don't
want to stress the existing board/driver.

Any suggestions on how to drive a bigger motor from the existing 4
wires? Power an external H-bridge? Convert to an electronic step
signal that I could use, after digital gearing, to drive a gecko?
Thought about mounting an encoder on existing motor to generate step
signals for a gecko/servo with identical encoder but I don't think
that would work. I don't know if encoder a/b pulses equate directly to
gecko step pulses. Direction is not an issue.

Roger