What if you put all of the quizzes into into a single Assignment Group. Then Edit the Assignment group to ignore the highest n-1 Highest Score. If there are 10 case logs ignore the highest 9. In this way if a student completes at 10 they get the score of the lowest (complete). If they only complete 9 or fewer, they are all ignored and they get a 0. To make this work you will need to ensure that any missing grades get updated as 0s, otherwise it will be as if the assignment is not required for them.

I just want to add that for at least 9 years I've been making fun of that feature in Assignment Groups to ignore the Highest Grades. I joke about how the only time you would do that is to tick off your students. This is the first real example of a useful case for that feature I've come across. I hope this works for you and I know I'm going to remember this scenario/use case now.
Rick
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