Locking quiz after students start taking it (Fails to update)

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In my synchronous virtual class, I want to open the quiz once review is done and then lock it so students cannot start the quiz later.  The whole point is to be flexible with the start and end time, so students can take the quiz then we immediately review it together.  But I always have students who start the quiz late, so I need to kick them out of the virtual meeting so they don't get the answers while taking the quiz.  

I tried locking the quiz, but it "fails to update". 

Any thoughts on what I can do?  Maybe changing the due time?  If I start a 5-minute quiz at 8:30am, when should I make the due time....8:31am (for starting the quiz) or 8:36am (for submitting the quiz)?