Failing to access AVR ATTiny13A with very slow clock (128kHz/128 or 128kHz/256) (avrdude: error: program enable: target doesn't answer)

Question

I am trying to program an AVR ATTiny13A using a USBasp adapter (guloprog) and avrdude. Uploading the program and running it works fine the first time for a fresh ATTiny13A device, but re-uploading again fails. avrdude cannot see/access the device at all. avrdude behaves like the device is not connected.

>avrdude -c usbasp -p t13 -B120 -U lfuse:r:-:b 

avrdude: set SCK frequency to 8000 Hz
avrdude: error: program enable: target doesn't answer. 1 
avrdude: initialization failed, rc=-1
         Double check connections and try again, or use -F to override
         this check.

avrdude done.  Thank you.

If I reduce the communication speed to the minimum supported by avrdude

>avrdude -c usbasp -p t13 -B2000 -U lfuse:r:-:b 

I get set SCK frequency to 500 Hz with the same result as above.

Looking at the programming signals with an oscilloscope, all signals look good, except for MISO which only shows rudiments of communication between 0V and 0.2V.

I have set the CKSEL fuses to 11, selecting the internal 128kHz clock source. In the program I set CLKPR to 8, dividing the 128kHz clock by 256, to get the slowest clock possible. (I have also set CKDIV8 to 1, but that should not matter.)

Have I fuse-bricked the IC? I do not have a HVSP to clear the fuses. What else can I do?