Ok, so this time I've unchecked "Allow the computer to turn off this device to save power" in Power Management (others were already unchecked) and in Advanced "Wake on Magic Packet" and "Wake on magic packet when syst..." (rest is covered) were already at Disabled from my previous attempts, so I've disabled the "Wake on pattern match" also. I'll test this combination for two nights and I'll come back to give you an update.
If someone else has a different idea, feel free to post it.
Thanks, Dave!