@futurebird apologies for replying to so many parts of this but one thing I can think of (noting I am not a trained teacher)
Are there any particular high performers or people who are normally finished before others in your class?
Can you enlist them to help out? I get this may go against wanting them to wait but it may stop or slow the barrage, or even encourage problem solving in the group.
I am definitely looking forward to hearing how it all goes. Best of luck - it's kind of endearing to hear students haven't changed that much since I was one.