Slightly belated update, but that managed to do the trick after some work! Some notes:
- The alternative computer I found (Z690 based) did manage to post with the old firmware (v4.9.416.0), but only if CSM was enabled. The system would hang if CSM was not enabled.
- The SMBus tape mode had no effect on whether the system POSTed.
- The offline ISO provided by HP would not boot properly, and hung partway through.
- I was able to modify the online version of OneCommand to install and run properly (minor modification to the system version detection install script and symlinking one of the libraries), but it would fail when attempting to flash the card.
- The method provided by @BeTeP worked perfectly with the latest offline ISO (12.0.1354.0), after updating the paths to match.
- After installing the flashed card into my original ASRock Z590M-ITX/ax, the first POST still took several minutes. Subsequent POSTs were much faster.