The GM throttle should be fine with the LED battery gauge disconnected, and the battery should have adequate output for a 3kW motor
(72V @ 50A = 3.6kW and @ 100A = 7.2kW).
Check out
this topic regarding a similar setup with intermittent starting.
Unfortunately, we never found out what was causing the problem as the original poster stopped responding.
It is difficult to say whether the humming is due to an incorrect Phase wire/Hall sensor configuration, controller fault, or possibly a very low starting current, but something is definitely wrong.
I would have expected the motor to run in a clockwise rotation
(when viewed from the output shaft end) which is opposite to what you have described.
I also recall a similar problem regarding occasional non-starting of a 5kW motor
(but only when it stopped in certain positions) which turned out to be a faulty controller.
You can perform a simple test on the phase wires and stator windings by disconnecting the phase wires from the controller, touching any two phase wires together, and then trying to spin the motor shaft by hand.
If the two phase wires
(and windings) are all OK, the shaft should be difficult to spin as the shorted phase wires will cause an electromagnetic dynamic braking effect.
The level of resistance should be identical with all three combinations of pairs touched together (Yellow/Blue, Blue/Green and Green/Yellow).
I have not tried this, but it might be possible to measure the voltage output on the phase wire terminals of the controller
(with the Hall sensors connected, but the phase wires disconnected) by applying the throttle while turning the motor by hand.
If it works, I would expect the voltage reading to be similar
(and the polarity of the reading should also alternate every 45 degrees) with all three combinations of pairs being measured (U/V, V/W and W/U).
This might not work as the controller may simply produce an error code if it is unable to sense any current flow because the phase wires are not connected, but if it does, you might be able to home in on any anomalies
(e.g. if one pair has a different voltage reading or does not change polarity as expected etc.)If you cannot find anything obvious, perhaps Gary could test your controller on another motor to check its operation.
Alan