A standard VFD, even a 220v one, can be configured to run that motor. All you have to program is the motor rated voltage and frequency and the V/F curve as linear. The controller will deliver the 120 v at the rated frequency. The sensor coil can be left disconnected.
To find the data communication protocol to the original controller board will be more difficult unless you could connect the main control board and simulate the unavailable machine sensors to be able to spy on the communications. That would not be worth the trouble.
To find the data communication protocol to the original controller board will be more difficult unless you could connect the main control board and simulate the unavailable machine sensors to be able to spy on the communications. That would not be worth the trouble.