FINALLY!!
I made CarPlay working!!! 
So, I wasn’t able to open up the center console (it’s complicated: https://www.youtube.com/watch?v=DoQIgoUalEo)
I called Ford parts and asked what’s the factory part number of the USB hub for my VIN. I was told it’s GR3Z19A387B, which is definitely different from HU5Z19A387C. Then I asked about the second part number and got lucky – they had exactly 1 of this in stock. I came to pick it up and got lucky again – Ford service installed it right away (they told me it’s not only swap – they also need to program it 
).
Anyway, Ford service installed and configured the new USB hub in one hour and I got my wired CarPlay working perfectly
BTW, the old USB hub part number happened to be GR3T-14F014-AB (not what Ford Parts told me 
, but still very different)
Then I plugged in and configured the Wireless CarPlay Adapter (I posted earlier: Amazon.com) – which also worked perfectly right away
(For future generations: link to correct USB hub on official Ford website: https://parts.ford.com/shop/en/us/electrical/control-modules/gps-navigation-control-module-interface-p-hu5z19a387c. @F150Chief suggested it’s cheaper on Ebay, but I didn’t risk it.)
THANK YOU guys for your help and support! 