For those interested, the reply from GIGABYTE came today.

To cut it short, they basically requested to remove battery and short circuit the "clear cmos" pins.
The reason the backup doesn't work, and I quote:
"However, if system boot failed, probably there’s something wrong during BIOS flashing and caused BIOS corrupted that would make secondary BIOS doesn't work either."

There is no mention of the faulty F5 BIOS in the reply despite me specifically mentioning it in the question (as well as the resulting infini-reboot).
To me, this reply is an insult.
They do not take responsibility and are showing disrespect to their customers (and not just any customers, the most high paying ones! I do not believe for a second that they are not aware of the faulty F5 BIOS they released, enough days have passed for everyone to be updated).

I am very happy I managed to unbrick my machine, I installed STEAM on it and ran a game for a few good hours to see that my system is stable.
I wish you all luck with your boards (be it with getting it back quickly from GB or trying the method to "unbrick" it).