Here's my recommendation: Turn off ALL NOTIFICATIONS for grading. You don't need them. Just check your To-Do List. Everything you need to grade will be there, including Classic Quizzes.
The To-Do List is your "best friend" in terms of grading. It shows Assignments (both original submissions and resubmissions), Classic Quizzes (anything not automatically scored), and graded Discussions.
The ONLY notifications I've signed up for is when a student sends me an Inbox Message or I send out an Announcement. No monthly summaries, no weekly summaries, no daily summaries..... All of these summaries are redundant, and I don't see any reason to clog up my email account with them.
Until your problem is fixed, why not just get a weekly summary, and then ignore it?