If your transformer neutral is grounded, you should have a neutral and a ground at the contactor. Right?
If both, neutral and ground, have odd voltages, then the problem must be where they originate - at the transformer.
The neutral and ground are connected to the transformer neutral with a lug. That connection might be bad. Some transformers have a bolt that goes through a fibre board that connects the transformer windings to the lugs. I've often thought they were a little loose right from the factory.