Cannot program ATTiny85 fused for 32 kHz
I figured it out. 

Fuse changes don't erase the flash. The previous sketch started with setting the system clock prescaler to divide-by-8. The clock prescaler survives RESET. 

The fix was to temporarily tie RESET low. That way I had a chance to attach the programmer and power up without the prescaler setting taking place.  I uploaded a new sketch without the prescaling and it works now.