In case it becomes relevant for anyone else with a Model 01, the ICSP connectors are numbered differently from the usual Arduino and AVR ICSP pinouts.
On the schematics and silkscreens, pin 1 is GND, while the AVR ICSP standard seems to have MISO on pin 1. The name labels and relative positions of the pins are correct, so rotating the connector (if you’re using a multi-conductor connector instead of individual jumpers) from what you might expect should work.
I’m glad I double checked this.
Somewhat relatedly, the Model 01 seems to present an electrical challenge for my Arduino Micro as ISP (too much current?); I had to dig out the Dragon and leave the keyboard powered on to get the ATtinys to do ISP programming reasonably.