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I believe that Jon is AA. A lot of why I think this follows a lot of what I've read in r/asoiaf on Reddit. Too lazy to list the evidence, but Google might help. Watch out for book spoilers. I also don't remember how much of the book stuff concerning possible hints appear in the show, so who knows how that'll play out there.
I too think that Jon being Azor Ahai would be both too obvious and fall in line with the prophecy being too on the nose.
Still, here goes with my speculation.
Based off of the book:
I think Jon does Warf in to Ghost and spends time in the far North, beginning to understand the true nature of the White Walkers, possibly with Bran's help. Eventually, he does get resurrected as Mel connects the dots but upon his rebirth he is not the champion of the Light but of the Cold, subverting the prophecy altogether.
Based on the show:
I think he is just reborn in the fire and becomes the new Night's King.
Either way I can't see him just returning to be Jon Snow again. All of the talk of "Jon Snow is definitely dead" on the internet and in interviews is their very literal way of playing with the audience. Plus, only in death does he no longer have to serve on the Night's Watch. Upon his return he is either something else with a bit of Snow's memories or he becomes Jon Stark.
Also.... wild speculation abound. I would not put it past Martin to have Arya somehow figure in to Jon's ultimate fate, with her either being the key to having him remember his past (As a Stark) or, and this would break my heart, as someone she has to kill to restore balance if he becomes too powerful.
Take care all.