I assume that the switch is to control the direction, so why don't you just wire around the switch?
How often do you plan on running the motor in reverse? I have encountered a similar issue with reverse units not working on Flyer prewar motors and if I cannot make them work, I wire around them.
From your wiring diagram, it appears that you would run the wire from the headlight to one of the brushes and the wire from the coil to the other brush. Just make sure that the motor runs forward. If it runs backward, simply swap the wires to the opposite brushes.