They don't make it obvious, but there is another way.
Updating the EEPROM is done by placing a "recovery.bin" executable file in the boot partition of the SD card along with the EEPROM image. On the next boot, the boot ROM in the Pi will execute recovery.bin which will update the EEPROM. Then recovery.bin renames itself so it will not execute again, and blinks the green LED rapidly to indicate success. It is necessary to manually cut power and restart, then the Pi will reboot back to normal operation with the new EEPROM. The recovery-related files can be deleted, since their data has been written to EEPROM chips elsewhere on the board.
The files are here:
https://github.com/raspberrypi/rpi-eeprom/releases/download/v2020.04.16-137ad/rpi-boot-eeprom-recovery-2020-04-16-vl805-000137ad.zip
Unzip the archive and copy the 5 files to your boot partition. This can be done either by mounting the card on a PC or from within OpenWrt by mounting the partition temporarily:
mount /dev/mmcblk0p1 /mnt
cd /mnt
unzip /path/to/zipfile
rebootThe instructions say to use a blank card, but that is not necessary. The Raspbian command simply copies them in addition to the kernel, etc that is already there.