Update: I repinned the final 6 pins as per Danep82's (THANK YOU!) diagram, and everything works perfectly now.
During my test drive, I was bummed to find that my GPS location was off by 500 meters (display showed I was driving in the ocean) and the compass did not work on the instrument cluster display. However, on my way back from the shop, it worked perfectly! I guess the navigation just needed a bit of time to calibrate my location accurately.
I also made some modifications to the FM antenna connector, as it did not fit the new headunit directly. The result isn't too pretty (I just shaved half a cm off each side and made a hole on the bottom for fitment) but it fits now and the FM radio works perfectly: https://i.imgur.com/dCa1dyK.jpg
Also, I had a lot of difficulty trying to find a suitable physical connector pin to achieve ground and IGN on the 20-pin connector. So in the end I just skipped IGN, which so far has not affected anything. I checked for continuity between the ground pin (pin 19 in your diagram) and the chassis of the headunit and of course there was continuity, so I just ran a wire from the headunit chassis to a screw on the car's chassis nearby. Ground achieved!
The final adapter cable I have isn't too pretty and if I were to make one again, I'm sure I'd make a far better one, but it works: https://i.imgur.com/cURftZl.jpg
I was so sure that this time everything will work that I buttoned up the car completely and put all screws and covers back in their place
Here is the final result:
On Monday, the dealer will try configuring (and calibrating I guess) the 360 cameras on the new headunit for me. That's the final thing that doesn't work. Fingers crossed.