See the attachment for the tech sheet.

You will have to do more troubleshooting.

Check the thermistor resistance.
If OK, see below.

Your live test tells you that at least one side of the line is getting connected.
But you do not know what side.
The heater relay side would be more likely so I would start there.
FYI: Even if the unit was running correctly you would still see 120 at all points when using Neutral/ground as the reference for the meter. Looking at the wiring diagram L1 would show up to the left of the heating element and L2 would show up on the fight side.

I think the heater relay and the motor relay are the same so I would swap them to see what happens. Double check that they are the same just to be safe.
If it now will not keep running when you release the start button replace the relay.

If this does nothing then remove the heat relay from the unit. Be sure that nothing can short to anything else.
Now do your live test again.
If you still get the 120 then you know that the centrifugal switch side (L2) is OK so there is probably a problem with the control board.