There were a series of dodgy internet travel agencies, some dodgier than others, who all claimed to be able to get this particular fare or one close to it (the lowest was $429.70). However once I tried booking the fare at one site after another I found that all but one refused to take my money saying the fare was unavailable.
As an aside, this is a problem with sites like Kayak, Fly, Momondo, and Skyscanner. They scrape other websites for fares but really have no way of telling whether you're actually going to be successful getting that fare when you go to the website they scraped. Still, they do give you some idea of what may or may not be out there, so that's something.
I figured I'd take the risk of handing them $508.50 given that the lowest available non-consolidator fare is $828.70 (direct from the airline). They've confirmed that they've taken my money, handed me a record locator in their system, and said I should hear back within 72 hours whether they've been successful in buying a ticket for me at the price they said they could buy it at.
Here are what I believe the rough probabilities are:
a) 5% chance: the agency turns out to be really dodgy, and runs off with my money. I am out $508.50 and still have to pay $828.70, for a total of $1337.20.
b) 85% chance: the agency turns out simply to be willing to take money when they're not sure they can get a ticket, and bounces my money with a "sorry, we couldn't get your ticket at that price". (I found a post about the agency elsewhere on the net describing just that happening to someone else.) I still have to pay $828.70, but I'm no worse off than before. And I would know for sure that the consolidator fare was in fact fictitious, expired, or otherwise unavailable from any source.
c) 10% chance: the agency actually has an ace up its sleeve in the form of consolidator ticket inventory that they can really sell me. I get that seat for $508.50, which is $320.20 less than the price from the airline.
The kicker in this is that the airline's website itself is refusing to sell any tickets anywhere at the moment, so there may actually be a glitch in its sales system preventing any tickets at all, consolidator or not, from being sold.† So that might be a contributing problem.
According to the dodgy internet travel agency I should get final confirmation email that they've bought my ticket within 72 hours. (During the week it's 24 hours, but this is a weekend.) 72 hours from now I should still be able to get the ticket from the airline itself for $828.70, as that fare is valid for a one day advance purchase.* Well, assuming they can sell any tickets to anyone.
†I do not currently have reason to believe that the airline itself has gone out of business.
*At that price buying the ticket with 30,000 frequent-flyer miles (plus associated fees) becomes a cheaper option, so I'll likely do that instead.
I guess I'll see what happens.