Make sure your normals are pointing the right way (recalculate your normals or just flip the ones that are backwards manually). Also, it might be that you are trying to bake the model without first having applied your mirror modifier first. This is most likely the cause of your issue. There are no overlapping UVs, but how do you think the mirror modifier works? It overlaps the UVs :P When you apply the modifier, you'll see what I mean.

Neither of those things fixed it. Anything else?

Maybe you have many materials, try to delete the material in the material tab and make a new one.

That did not work either.