Half my class threw paper during a quiz. How would you handle this?

I'm a first year teacher. Today during a quiz, about half my class started throwing paper balls around. The environment got loud and disruptive enough that I genuinely don't think the other students could focus and do their best work.

Important context: I explicitly told the class before the quiz started that anyone who spoke during the quiz would get a zero. I made it clear. They knew.

I wrote down the names of every student who threw paper. I know exactly who did it. I have already write them up and wrote up the students talking

I can't split the room or do detention make-ups easily due to scheduling.

My current plan:

· Toss today's quiz entirely (not fair to the kids who were trying)

· Give a new quiz tomorrow on the same material

· Deduct 10 points from the throwers' scores on tomorrow's quiz

· Warn the class beforehand that any disruption tomorrow = automatic zero

But part of me feels like since I already said speaking = zero, I should actually follow through and give the throwers a zero on today's quiz, or make them redo it tomorrow, or both? 

Is that too much? Or is that just following through on what I said?

Thanks in advance.