I would place slightly more stress on the word "right" but not much. "Do" would still be the strong form of the word, as you've indicated in your transcription.
And I would also agree that "do right" is not a phrasal verb. Something is only a phrasal verb if the adverb changes the meaning of the verb. In this case, the literal meaning of "He does right" is "He is right to do it." In both cases, the verb is "do" and the meaning is the same.
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