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I am in a similar situation. I am a postdoctoral research fellow with a J-1 visa and I received a 1042-S form from Columbia University. As a Spanish citizen who has been here less than 5 years, I am aware of the existence of a Spanish tax treaty regarding the 1042-S, exempting me from Federal and state taxes. I was following the method described above ( @AmyC  method), but I have some concerns:

- This approach doesn’t seem to include any details about the "employer"/withholding agent. Isn’t that information important when filing?

-My taxes withheld are $0 because my university already applied the treaty benefits. However, when I follow this method, the New York State return shows a refund of $63. How is that possible if I haven’t actually paid any state taxes?