How long does it take to produce a portrait?

I'm confused by the portraits that hang in the Hogwarts headmaster's office.

Okay, maybe I'm not confused by the portraits themselves but I'm confused by the process by which they are created.

And especially how long it takes after the death of a headmaster for his or her portrait to appear.

As we all know (I won't give a 'spoiler alert' since anyone who has read this far into this entry must have read all the Harry Potter books at least once), Dumbledore dies near the end of The Half-Blood Prince.

If I understand the 'Avada Kedavra' curse properly, it kills the instant it strikes its victim. So Dumbledore was dead even as his body was "blasted into the air" by Snape's curse, before it disappears over the battlements and ends up lying at the foot of the tower.

By the time Harry makes his way with now Headmistress McGonagall to the Headmistress' office just 27 pages later (in my paperback edition), Dumbledore's portrait is already hanging on the wall behind the desk. I take it that the position directly above/behind the desk is the place of honour for the last Headmaster but I may be wrong about that.

In those 27 pages, Harry fought his way out of the castle in pursuit of Snape, engaged in several duels with Snape and others, helped Hagrid put out the fire that was engulfing his house, returned to the crowd surrounding Dumbledore's body, then made his way up to the hospital wing to see poor Bill and sat with the Weasley family through Fleur's revelation of the true depth of her love for Bill.

Let's say that entire process took, what, two hours at most? Perhaps not even that long since Rowling says that the office, when Harry and McGonagall enter it, "looked exactly as it had done when he and Dumbledore had left it mere hours previously" and those "mere hours" also included the fateful trip to the cave for the locket.

Okay, so the process of creating a portrait of a headmaster takes at most two hours from the moment of death to the appearance of the portrait in the office. Right?

Now let's move forward to The Deathly Hallows and (no spoiler alert) the death of Headmaster Snape.

Snape dies of wounds he receives from Nagini.  Immediately thereafter, Voldemort calls for a cease-fire in the battle and gives Harry one hour two join him in the Forbidden Forest, or else the Dark Lord will join the battle himself.

Harry goes almost directly to the Headmaster's office to use the Pensieve. When he gets there, he finds every portrait absent, every frame empty. Harry "glances hopeless at Dumbledore's deserted frame, which hung directly behind the Headmaster's chair". So it hasn't moved to make room for a new portrait, one of Snape. And there's no mention of a new frame, even an empty one, where Snape might have hung.

Okay, so Harry takes a full hour to view Snape's memories, gird himself and walk into the Forest to face his death. He confronts Voldemort just as the hour expires. It would appear that the scene at King's Cross with Dumbledore takes no time whatsoever, since Harry returns to the Forest mere seconds after his duel with Voldemort.

So we're still at an hour. But then there follow a series of scenes that take some time. In fact, when Harry finally defeats Voldemort, the victory occurs just as the rising sun bursts into the Great Hall. So it's morning.

And Rowling then writes that "[t]he sun rose steadily over Hogwarts, and the Great Hall blazed with light and life." News comes in from every corner "as the morning drew on".

So, by the time that Harry, Ron and Hermione finally make their way to the Headmaster's Office for their final chat with Dumbledore's portrait, anywhere from three to say 12 hours have passed since Snape's death.

And yet... no sign of Snape's portrait. Dumbledore still sits in the "largest portrait directly behind the Headmaster's chair".

If Dumbledore's portrait can appear in two hours or less, why does it take so long for Snape's to appear?

Four possibilities: 1) Snape's portrait is there but Harry simply does not notice it and Snape chooses to say nothing; 2) Snape's portrait is delayed because the portrait painter is otherwise occupied (in the battle and the celebration that follows, perhaps): 3) Snape will never get a portrait because he was not a true Hogwart's headmaster; or 4) Snape isn't dead.

With regard to 1), I doubt it. Harry would notice it or at least Snape would not be able to stay quiet. I would also think that Harry, having seen all that Snape had done for him, would have taken the opportunity to thank him at the end of the book.

As to 2), I guess it's possible. I always thought that the portraits were produced by some magic of Hogwarts itself, not by an individual witch or wizard. But it is possible it was delayed.

I don't buy 3) because Harry himself, in the epilogue, tells little Albus Severus: "you were named for two headmasters of Hogwarts. One of them was a Slytherin and he was probably the bravest man I ever knew." So Snape was, indeed, a Headmaster.

As for 4), hmmm.... In describing Snape's death earlier, Rowling wrote: "after a second something in the depths of the dark pair seemed to vanish, leaving them fixed, blank and empty. The hand holding Harry thudded to the floor, and Snape moved no more." Snape sounds pretty dead to me.

So I guess it must be 3) after all. What do you think?