I freaked out because I thought I bricked my 5D3. Turns out there is a missing step in the instructions.
Make sure you take your 2nd card (SD in my case) out of the camera... Otherwise the camera will go blank and not respond to anything when you start the upgrade. It looks and smells like a failed upgrade that bricked your camera :-(
If you read this too late then here is your rescue:
Remove your CF, delete the firmware from the CF via your computer, put CF without FIR back in the camera, remove battery, put battery back in, wait for error message about missing FIR file, put CF back in computer, put FIR back on CF, put CF back in camera and finally exhale (and go change your underwear because you know you nearly S___ 5 minutes ago).
This worked (rescue procedure above) for me, and then I was dumb enough to try again (without SD card in) and it worked fine.
Laugh all you want, but that Samoan timezone and Finnish menu fix were ruining my workflow. I'm good to go now.