I've now made some progress with the "Submitted" state, where an attempt as been submitted and is awaiting the asynchronous grading task to run. As Tim suggested, this mostly "just works" with a few minor modifications.
The review page looks like this:
And the quiz view page like this:
Once MDL-70854 is integrated, we can enhance these screens by showing the status of the grading task.
For the purposes of access rules and completion criteria, "Submitted" attempts are treated the same as "Finished", so if the quiz is marked as completed after you have made 2 attempts, it doesn't rely on those attempts having been graded, for example.