I’m considering the concept of adding in a dropdown/select box above the “Active Projects” portion of the front page that contains all your Spaces. Then you can pick a specific space to filter and show only project/task pairs from that space.
My only concern is that if someone stayed on a single space filter for too long they could lose track of projects/tasks on other spaces, but maybe I could do something in the UI to help communicate they’re viewing a single space and that other projects need action . . .