Just got off the phone with the US Apple Support. I thought maybe I could get the rules bent a little in the USA, particularly since it was a US-bought product. But they don't love me anymore either.

They said letting any hardware go out of warranty, and not opting to buy Applecare is essentially a gamble, and that they're unable (unwilling!) to make an exception. So, in short: 500USD iPod Touch is really only obligated to work for 12 months, after that, enjoy your hockey puck.
OK, I tried.
Having already spent a day in Osaka attempting to address this, I'll now follow up on the OOW repair place in Nipponbashi, pay whatever they're charging, and live with the results. Failing that, I may mail it to a US OOW repair place and have them ship to a friend's US address, then have it shipped to Japan. Golly, I love the convenience of using Apple products.
