UPDATE:
1- I created a copy of my Library (drag and drop to another disk).
2- I went, one by one, (NOT FUN), through all my 1791 songs, and made a list of those that were not opening on BBMO. I confirmed that they worked PERFECTLY FINE, on the BeatBuddy pedal, and also, when I opened the copied library, on BBManager (legacy). The issue was only on BBMO.
3- I went on to re-construct the error files. Opened both BBM (with the copied library) and BBMO (with my production library). After unsuccessfully trying to import to BBMO a newly exported .sng file from BBM, I decided to manually export the midi files, the real content of the songs. SO, a) I created a new empty song on BBMO, b) manually wrote the tempo and drumset info, as it appeared on BBM, and c) imported the midi file into it. That is, I exported the midi file from BBM, and imported into the newly created empty song in BBMO.
30-ish reconstructed files later, it was time to try and use the csv tool from @andrew13 site. Eureka! It instantly processed my library and I was able to download the new csv file.
So, you cannot have reading errors on BBMO, or your library will not open on the Exporting tool.
The mystery remains, why does everything works just fine on BBM, and on the BeatBuddy pedal, but NOT on BBMO? What caused the corruption?
But on the happy side, the exporting tool works as flawlessly as ever, and now I have a clean library.