It's always better to take care of these issues while in the USA, otherwise these gray areas and problems might surface. I would still think that the correct form is N-600, but the instructions of N-600 clearly say not to use it for children who regularly reside outside of the US. However, N-600K doesn't seem appropriate as the child already got a passport and got citizenship by operation of law when the parents naturalized in May. Perhaps the cover letter might help. I would assume the child might have to make a trip to a USCIS office at some point, perhaps a consulate, but not clear which. I don't think the original poster did anything wrong, it's just that it was done in a way that the bureaucracy doesn't seem to know how to deal with it.