Ok, it works! I have no time to package it right now, so I'll upload it here for the impatient. Feedback via PM while I put it on openrepos, so we don't clog the thread

This is the first version with the Paisa corpus and with the dictionary coming with Ubuntu (/usr/share/dict). This dictionary is the only reasonably sized (ca. 90k words) I could find without obvious spelling errors or wrong accents. I'll do my best to merge the corpus kindly provided by ferlanero, in case Paisa is not enough.
Feel free to provide any better dicts or corpora.

Thanks to everyone involved for the great help.

File:
https://www.dropbox.com/s/bp73u54k0qgwpul/ita.gz?dl=0
Instructions: extract the contents of the tar in ~/.local/share/okboard/
No need to reload the keyboard, it will pick the files up automatically as soon as you switch to ita.