I would like to see support for some Kanban Classes of Services integrated into this app (see e.g. https://leanandkanban.wordpress.com/2009/06/10/classes-of-service-and-policies/ ).
So, each item could be assigned a class of service. For example, ”fixed date”, expedite, normal (rising linear cost of delay), depreciating (dropping linear cost of delay).
The app analyzes all items’ classes of services and creates a prioritization of all items, which is then visualized as you described in your mockups.