Thank you MHG! Looks like I've been stressed out more than I should be about this issue :P.
I donīt understand why you should not be able to get the visa sticker in your new passport and stamped in Spain. Since you have your new passport in hands already your local immigration office in Spain should be able to just put the visa label in your new passport - no need to go back to NYC for that ...
The local immigration office has access to the Schengen immigration database. And since you reported the loss of your previous passport to the immigration (I suppose you did that ...) there should be no fuzz about issuing a new visa sticker in Spain.
The document from the NYC consulate may be helpful for that - but not for travel in the Schengenzone as non-spanish immigration officers are unlikely to accept a notice from the spanish consulate in New York - other than a proper visa!
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This is exactly what I thought at first, because the immigration office should have my info in their database right? But when I called the consulate, they told me that the only way I could get a new visa sticker is to go back to NYC and have them stamp it in my new passport.
Anyway one more question: do airline staff (or anyone else at the airport where you depart, you know, those people who check your passport when you're in line for security scanning and boarding) have the right to refuse to let you board because of something related to visa?