Tech's troubleshooting reports no open neutral, and the fan has an open connection with no visible damage. He also reports that the fan housings seem a little on the warm side.
Sounds like just a defective fan motor from here. A shifting neutral would probably have fried the motor violently and also killed the speed control.
As for your voltage readings, take them with a huge grain of salt, so to speak. If the control is electronic, in addition to chopping the wavewform, it would possibly increase the voltage to compensate for lost motor torque.
OTOH, you could have also been reading "inductive kickback" from the other fan's motor.
And as for the housings seeming "a little on the warm side" remember a normally operating modern motor can safely run up to 40 deg. C above ambient, more than hot enough to burn your hands!!
Replace the bad fan and move one.....