OK, so we can do with with a reverse relationship. You want to lookup data from a child record to a parent record, so we need to figure out who the lucky Task child is which is Active and and then make him a Parent.
First we figure out who the lucky child is.
On the relationship where 1 Project has Many Tasks, make a summary minimum of the [Record ID#] where the the filter is that the Task is Active. Call it [Record ID# of Active Task]
The Project now knows the [Record ID#] of the Task that has the info we need.
Make a Relationship where 1 Task has many Projects. Yes that sounds backwards, so that is why it is called a reverse relationship. On the right side, do not let it create a new field, use the field we just made called [Record ID# of Active Task].
Then just lookup any fields you need from the Active Task to the Project, such as Task Owner and Task Status