How about adding the option "Unlimited improvement attempts" to the "Attempts allowed:" drop-down at the "Editing a quiz"-page?
With this I mean that the students' responses from their previous attempt will be filled in as default. Correct answers could perhaps be locked.
The existing option "Unlimited attempts" has a simular impact but does not save the students from redoing already answered questions. In case of numerical problem questions that involve heavy calculations, where answers can depend on previous answers, this could save the students from the task of retyping their already determined answers. That way it would also be more natural for students to have early question results verified before they use these possibly corrupted results for solving latter problem questions.
Anyway, we want this functionality for a statistics course this fall and, unless someone suggests a better solution, I will dig into the code pretty soon.