Question
our chazzan is now a rabbi also...
and has both ’ordinations’/’smicha’...
how to address him properly in writing
would rabbi-chazzan xxx be appropriate
Answer
ב"ה
Shalom
First, I should is admirable that you are concerned with the fine tuning of how to address a person who is a Rabbi so as not to show any disrespect. There is much to be learned from that.
I think it would be fair to say that we view being a "chazzan" as a profession, while the title "Rabbi" is a title of honor which we are instructed to uphold to show respect for the Torah which is personified by the Rabbi. If he is your officiating Rabbi, it is proper that the title Rabbi come first as you suggested.
I think the rest is up to English grammar and what you want to emphasize in your sentence. For example, if you were to say, "Our chazzan, Rabbi so and so.." it would also be fine.
All the best
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