How much current is a powered-down ATtiny84 supposed to take?
This comment on reddit pointed me to this page, which says that clearing the ADEN bit in ADCSRA shed as many µA as are currently in excess in my test rigs. I am away from the lab right now, but when I get home tonight, that's the first thing I'll try. I'm optimistic. I do know that the ADEN bit gets set in init() in wiring.c...

If it's confirmed, then the lesson is that PRR is not enough to turn the ADC all the way off.

EDIT: It is confirmed. The one added caveat is that order matters. ADCSRA must be written before PRR.

My sleep_tiny_sleep sketch (last above) now takes &lt; 100 nA.