I don't think the motor is faulty since it runs fine every time in agitation mode. The same motor windings are used is drain/spin as are used in agitation but motor direction of rotation is reversed by reversing polarity to the start windings. This is done via the timer and that has been replaced. It may be a lid switch problem as the lid switch is only used during drain/spin. Remove the cabinet and bypass the lid switch as shown in this video. Your switch is the second one in the video. Place washer in spin mode and see if the clutch hub is spinning. If the motor is just humming, is the motor shaft rotating or not? Another possibility is that there is something in the drain pump causing it to jam intermittently which will also prevent the motor from rotating as the pump is driven directly by the motor shaft.

Eric