There is not an Instructure deadline for migrating to New Quizzes, @Universitygeek .
To answer your question, I wonder if the Classic Quizzes that are working after import are set up with links to a Question Bank. Here is a screenshot of what that looks like in Canvas:
Group with link to Question Bank
This quiz has a Group ("ch18") that pulls 5 questions from the bank "ch18-yes."
Migrating this Classic Quiz to a New Quiz does not also migrate the linked Question Bank to an Item Bank, which severs the connection between the quiz and the questions. Not very fun!
Another way to set up a random block is to create a Group within a Classic Quiz, as in this screenshot:
Group with questions within a Classic Quiz
This group is named "ch17" and also will select 5 questions, but in this case all of the questions are within the Group within the Classic Quiz.
The workaround I developed is to move the questions from the Question Bank into a Group within the Classic Quiz and then migrate it to a New Quiz. The group-within-a-quiz then becomes an Item Bank, which is the New Quizzes semantic equivalent to Question Banks in Classic Quizzes.
I hope that the conversion from Question Bank to Item Bank is made mode seamless, especially for situations like these.
I have prior experience with Blackboard and have a memory that Blackboard's random blocks work similarly (a link from the quiz to the group of questions), which is why I think you are encountering the same thing. Does this suggestion make sense?