After failing to upgrade a standalone 3.06 FW13 12th-Gen Intel mainboard to 3.08 in January (12th Gen Intel Core BIOS 3.08 Release - #662 by Anthony_Garrett_Guil), I again attempted the EFI upgrade method following the standalone instructions on OP and experienced no positive change in behavior from my last attempt.
PD upgrades still work without issue, but the BIOS upgrade still fails at the same point (the “After PD updates, it will reboot automatically, then start the BIOS capsule update” point in OP’s instructions; the reboot occurs, but the BIOS capsule update never happens).
Nearly identical messages are reported as the 3.08 failures: Error 331: Full FW Update using same version is not allowed. Include -allowsv in command line to allow it., Succeed to write Framework_Laptop_13_12th_Gen_Intel_Core_capsule_signed_allsku_3.17.cap.
The only significant change in behavior is that the system now reboots after each failed attempt instead of shutting down, which leads to an endless loop of failed upgrade attempts if left unattended. The only way to stop it is to pull the upgrade media between reboots.
A video of one complete loop of failure:
I’m still on 3.06 as a result.