Seems to me that if you want to have an individual due date for any question type, you would just need to do a one question quiz with a due date and time for the quiz.
However, if you use a countdown timer bundle with the Generico filter, there is no need to change any Moodle code. You just add the Generico filter with Countdown Timer directly into the question. Just like any other quiz with a deadline, you would need to set the countdown timer deadline in each quiz before you use it.
