Sounds about right to me. There a four screws on every Schumacher gear diff, they're all the same. Either side of the correct holes for the screws are another hole which isn't quite central to the screw hole, if you try and use these you will have issues.
You could strip and clean the diff and then maybe with a white marker pen colour in one half of the diff casing where they should touch together and see if they are actually touching. If you have it engineers blue would be the best for this.
How old is the car? Maybe worth speaking to Schumacher, especially if you brought it new and recently. Maybe you have a defective diff casing with some porosity, get a new one.
Could you post some pictures of the diff built and stripped?
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