Did you end up booking AZAL? I flew AZAL FCO-GYD last week but it wasn't a widebody. BTW, when I was researching AZAL, I saw that you can obtain a visa upon arrival ONLY if you fly the JFK-GYD flight. That may be a good option for you if you choose to stopover in Baku. Note though if you have any passport stamp indicating you were in Armenia, they'll ask you questions.
As for my flight on AZAL, it was less than half empty. Each one of us had our own row and I was quite surprised the flight wasn't cancelled. I'm not sure about the JFK-GYD flights but I suspect those aren't that full either given the prices to TLV. I saw cheap prices JFK-TBS via GYD as well.