Does anyone know if there's any software of any kind (app, script, program...) of any platform that allows mass deletion of Facebook conversations?
No, there is not. Facebook applications can only delete content they own/posted. In addition Facebook doesn't deal in the negatives, so applications like these are swiftly banned/deleted.
Even if you got a script to automatically click delete in a browser simulated window, your account would be disabled faster than the script would finish.