I don't understand. Repair what failed on the existing motor controller.
How did you let the smoke out? It may need some engineering rework, maybe a 20 cent more expensive (transistor?) or heatsinking to it improved or XYZ, but odds are that the path of least resistance is repair and improve what you have instead of reinventing the wheel.
If you really want to downgrade the functionality, since you have tested that it works with a DC low voltage source, then you need to determine a (rough) estimate of what voltage it needs, then proceed from there with a DC motor speed controller.
If the entire board or whatever you are comfortable with using is trashed, then you will need to build or buy a circuit to adapt the AC input to the DC level your chosen controller accepts. There are many variables, multiple ways to get to a result that is just a certain speed for walking.
If you want the simplest solution, it would be to estimate what % of the speed you need is achieved by the particular battery voltage you used, then you determine the target voltage for the target speed. Then you use ohm's law to determine current but better to overshoot that, since voltage determines current in this resistive load application. Once you find your target voltage and minimum current, it is easy enough to buy a SMPS to meet that, but as above I would rather fix the fault and have it fully functional again but improved so that the chances of same failure happening again are reduced.