Can I filter jobs by due date and exclude ones where the period end is in the future?

Not directly. The due date filter looks at the internal or statutory deadline, not the period end date.

Go to Settings > Jobs > General Settings to choose whether this filter shows as a deadline date or a number of days forward.

To see older periods first, sort your job list by period end with the oldest periods at the top instead. This will not exclude future period ends automatically, but it puts them at the bottom of the list.