Hi Rick,
Thanks for your reply. Those are good questions. I hadn't thought about how grades might be represented and how other parts of Moodle might be affected.
I thought there might be two ways to implement what I wanted: either as part of the grading or as part of the completion criteria. Assuming as part of the grading, we would need to set a minimum attempts required which would default to 1 and always forced to be equal or less than (maximum) attempts allowed, probably without the unlimited choice as well. For grading method the most meaningful method would be 'average grade' but it would be better to display extra information like 3 of 5 attempts to the teacher and students in the most detailed gradebook reports. There definitely needs to be some way of indicating the quiz activity is not passed or completed yet. If done as part of the completion criteria, there is a checkmark shown to the student when an activity is completed. (The logic would be number of attempts >= minimum attempts required AND grade >= passing grade.)
As for enforcing a minimum delay times between attempts, nothing should change there. The teacher can set that as they wish. I personally enforce some time between quiz attempts. But as the contents of each quiz can be independent through randomization, there is no need to force it.
As for the calendar and upcoming events, do they look at whether a quiz is passed or failed for passing information to the student? I don't use the calendar very much. I also don't use the Timing setting for opening and closing quizzes. In my case, I let the students have access to the quiz for almost the entirety of a 4 month term. I imagine people who want to use a quiz activity in a narrow window of time would probably not bother to enforce a minimum number of attempts beyond 1.