John Fitzpatrick has an interesting answer to the very last question at the end of his AOU presentation here.
Someone asked about Ivory-bill population demographics, and Fitzpatrick said that some calculations had already been done to answer this question: "How many would there have to be around the South to make it possible [for them] to have existed with some degree of confidence to the present?"
The answer was about 20 or 30 birds. Fitzpatrick called this answer "intuitively, a fairly comfortable one", and I agree. That means that for the Ivory-bill to live today, a population of tens of birds must have avoided confirmed detection for 61+ years now, which seems highly implausible to me.
Of course, that would also imply that current Ivory-bill searchers are most likely looking for a population of at least 20-30 Ivory-bills, rather than seeking a single presumed impossibly-wary ghost bird ranging over an 800+ square mile area.