According to a posting at TAF's Japanese blog, tickets have become available for purchase. This information is missing from their English blog, and I can see why. None of the services they linked is set up to deal with foreigners; I was even unable to register (for example, foreign telephone numbers are impossible to enter). Most likely, they won't send my tickets to me.
I am not willing to take a risk of just showing up with cash at Big Sight and trying to buy a ticket at the entrance (from a scalper, perhaps). But I don't have to: all I need is to ask a friend in Tokyo to buy tickets for me, call upon him (or her) when I'm there, pick up my tickets and give him (or her) a suitable present and feed him (or her) a meal or something. This is what I would do if I travelled to St. Petersburg. There's only one little problem: I don't know anyone in Tokyo. Other than that, a perfect plan.