hm... I have now changed the request ISR on the Attiny84 to this:
TinyWireS.send(sendData[i]);
i++;
if (i == 8) i = 0;
This has brought a slight improvement, as the Attiny now apparently actually gets polled a few times by the master; but after a few turns, the LED stays LOW again (in my sketch, the LED goes low when an I2C request is incoming) and then stays low. Normally, after the I2C transmission is complete, it should go back up to HIGH. So it seems it's crashing again on the I2C request.