Hello Geoff and John!
Thank you for very detailed answers! It helps a lot to know that I'm not alone, staring into the darkness of the MIDI abyss
So here is a more detailed explanation of the behavior of the unit:
1) A note is played, as soon as the said note is stopped, a Note-Off message is sent along with the All Note Off message.
2) If another note is played, while the first note is still sustaining, everything works as intended; the notes are allowed to fade out gracefully (as long as at least one note is still sustaining), then the deadly All Note Off is sent.
3) If the Hold function is used (by activating the FS1M switch, which took me 6 months to find

), the unit behaves like a piano sustain pedal (allowing me to stack multiple notes, even when my finger is off the string), but the infamous All Notes Off is still sent... Also, activating the Hold function by default, will render playing the instrument almost impossible, since every note will keep resonating (while the All Notes Off will still be sent out...)
I will read the manual again, but I'm not sure that there's anything in the MC1 unit that is user-configurable, unfortunately...
Thank you again very much, I really appreciate your help!