I don't know enough about the internal file system to offer intelligent technical advice. I seem to remember that /USER is on a separate physical device (NAND) and is mounted under the root file system - like with Linux. I assume PRG0 and PRG1 are just directories on the USER NAND.
I also just took a look at my a backup SD with my /USER files and I see you are missing more than PRG0 and PRG1. Besides SYSTEM, I also have RW and SETUP directories. However, those may be recreated as part of the update installation. Also, there are lots of subdirectories in /USER/SYSTEM. Some of them may be missing on your unit.
My only thought is to see if the failure is cause by the fact that neither PRG0 or PRG1 directories are present. So - try running testmode and manually creating them in /USER. I noticed in your video that there was lots of activity reading the SD before it errored. Maybe it was at the point where it was trying to load files in the missing directories.
Update: I played with testmode for a while - that are many other diagnostic functions besides file maintenance. There is also a way to examine error logs. BTW, in testmode main menu, use the < > arrows to see several more pages of diagnostic tests. One of test is a NAND test. Use care with this - it can be destructive. But you can do a read test of the sectors of the USER NAND. It takes a while - don't run down your car's battery - Porsches are a pain if the battery get's too low and you can't open the front trunk to get to it (ask me how I know).
Other useful diagnostics might be Forced Write and Drive Maintenance. I'm not about to play with these powerful - yet dangerous functions on my good head unit.
However you might not have much to loose. Just back up USER first.
If all else fails, send in your unit for service. It might be as simple as re-imagining all the firmware.