Our team also depends on being able to have these due times front and center. Our current workaround has been clicking on the Task Summary in the My Task widget.
But this has not be well received, so some users have move over to using dashboards to fulfill their needs because this adds additional clicks to their workflow.
If your team is trying out the the new Priorities area, I was unable to locate the due time at all, so this area is currently not helpful for my team and we disabled it.