I like the "student still has to submit' option when the time is up.
It is in the spirit of "student in control" and "good attitude".
We had a room where the teacher could take over the pc-control and - even as a group of teachers during a meeting - you do not like that when somenone really does that.
(small message on the bottom: "start and endtime for this quizz are registrated on the server, this timer is an indicator for you.")