Finally found the solution to my problems.
First of all, here is a completely working EFI for Catalina on ASUS N552VW-FI202T:
https://github.com/xXConcasXx/asus-n552vw-catalina (downloads are under Releases).
Anyway, the EFI alone is not enouth, what really made it for me and allowed me to finally boot correctly was the BIOS version: if it's 300 is fine, any other is not (including the latest, the 304).
So, should you need to downgrade the BIOS, I got you covered: first download the 300 BIOS from here
https://www.asus.com/it/Laptops/VivoBook-Pro-N552VW/HelpDesk_BIOS/ and then flash it using Windows, with the aid of the official ASUS tool, WinFlash.
Obviously WinFlash checks if you are trying to install an older version and stops you, but that can be bypassed using cmd and starting the software using the "nodate" flag, which allows you to flash any BIOS firmware you want:
cd "C:\Program Files (x86)\ASUS\WinFlash"
WinFlash.exe /nodate
Once the firmware is flashed, both the installation and the subsequent macOS boots should be fine.
Thanks for the help you have given me, I hope that I have been clear enough.