A good post, with a good request for help, very well explained.
I will try not to extend this post too much, because there are many things to tell about my experience with my Navigon.

Firstly, my messages are translated with google translator, there are some words that are not translated correctly.
Second, I don't have any Navigon PID / Garmin PID.
To try to help you, what I can contribute is my experience with a Navigon 70 Plus:

Quote Originally Posted by Grodan View Post
...a Garmin 10R-04 6953 4NSF, branded for Volkswagen. From what I understand it's really a Navigon 70/71...
Yes, it's from the Navigon 70 xxxx family...but the hardware is different, for example the RAM memory:
  • NAVIGON 70 Easy Europe 20 = (64mb RAM)
  • NAVIGON 70 Plus EU 20 = (64mb RAM)
  • NAVIGON 70 Plus = (64mb RAM)
  • NAVIGON 70 Plus Live = (??mb RAM)
  • NAVIGON 70 Premium = (128mb RAM)
  • NAVIGON 70 Premium Live = (128mb RAM)
  • NAVIGON 70 Premium Automotive = (128mb RAM)
  • NAVIGON 70 Premium Caravan & Truck = (128mb RAM)

I imagine that Navigon PID/Garmin PID has ???128mb??? of RAM...

Quote Originally Posted by Grodan View Post
...Got a starts up with VW logo and three rows about firmware version, then halts.
If I reset it to factory settings I get the white screen for calibrating the touch screen afterwards. At this time it identifies as GARMIN GPS in the Windows XP computer (not recognized at all in Windows 10).
When the screen calibration is done - I get the icon with the unit connected to the computer...
Well, here is the part that explains my experience with my Navigon 70 Plus.
Buy my Navigon 70 Plus +/- 11 years, after 2 years I decided to buy map updates with Navigon Fresh and update the ROM (Firmware + Software) also with Navigon Fresh, the result:
The maps were updated, but with the ROM update, the GPS was a little slower, until one day it crashed, restarting, it didn't solve anything as you explain in this topic about your Garmin PID, connecting to the computer didn't solve anything, do reset doesn't solve anything, charging the battery doesn't solve anything (the pc's power is not enough to charge the device, it only maintains the charge necessary to make the updates/modifications), disappointed with the situation, I turned off the GPS and put it in the box, until one day with availability, I attacked again, I spent 3 days installing and renovating, in my case the solution is very simple to turn on the GPS and let the battery discharge by itself.
My opinion and final conclusion about this bug is due to a hardware and not a software problem, today the GPS works at 100%, but a few times a year (depends on the use) the GPS blocks, the solution is to turn on the GPS and let the battery discharge on its own, +/- 24h to fully discharge in standby mode.

Quote Originally Posted by Grodan View Post
...Now the Garmin device is no longer present but instead two USB devices called:
NAVIGON WOLF_FLASH USB Device
NAVIGON WOLF_SD_CARD USB Device
They appear as two removable devices but these just opens empty windows and nothing (that I tried) can be saved to them...
Without Navigon Fresh/garmin Fresh, this is ok, as it should appear on the PC, but first you must solve the memory BUG as mentioned above (discharge battery).

Quote Originally Posted by Grodan View Post
...Not sure I have the proper drivers, I installed the ones Garmin offers on their driver page...
No problem with the controllers, I use Windows 10 and I have no problems, again I repeat, discharge your PID battery for 24h, charge the PID battery again with vehicle power (not PC), try to synchronize again your PID to PC.

Quote Originally Posted by Grodan View Post
...Also tried adding the files for rebranding a navigator from Seat/Skoda to VW, which is activating DevMode as far as I understand...
????

Quote Originally Posted by Grodan View Post
...I got "Cure" as well, even if it works with this navigator I have no firmware file to use with it.
RMPrepUSB was not included in that package, GarminCure3.exe and Updater.exe with a pdf that has instructions...
None of this applies to your PID model, don't confuse Garmin GPS with your PID model, garmin GPS uses its own operating system, Navigon PID and Garmin PID use WinCE, for the simple reason that Garmin purchased Navigon and was able to maintain Navigon support until last year, so don't complicate your life and don't make the situation worse, do the above and leave the Garmin GPS programs and firmware aside.

Quote Originally Posted by Grodan View Post
...It seems it's the navigator itself that renames the microSD card to "NAVIGONSD" after a factory reset...
"NAVIGONSD" doesn't include any software, it's just used to pass the maps from the internal memory to the SD in alphabetical order, to start the software from SD, you must start with an "UpdateMe.exe"...

See if you can re-establish PC connectivity, we'll talk later.