You still have not posted the connection diagrams for the motor or for the drum switch that I asked for. There is no real standard for how motors are connected. Or how drum switches are connected. Nor for the colors of the wires coming out of the motor. Every or almost every manufacturer did it a different way. But the fact that at one place in the wiring you have half line voltage tells me that the motor is definitely connected for 240 volts, not for 120. There is no other way to get half of the AC line voltage in a single phase AC motor.
You need to have someone who knows what they are doing rewire the thing before you electrocute yourself,