Notification/Filter for authorised invoice with no email sent

We want to have a notification that informs us when a sale has been invoiced, but an email hasn't been sent after a set period of time. This could also work as a filter instead where it filters by Invoice email sent/Invoice email not sent.

We don't want this step automated where we invoice the job it automatically emails the customer, as we often have customers with unique requirements that require different email addresses for different orders, and may require different text in the email being sent.

I see the notification of Authorised sale quote has not been sent to customer, but this only works if the customer isn't emailed or printed. In our current process we print the invoice which invalidates this notifications.

Could it be possible to have a notification that notifies us if the customer isn't emailed?