If the goal is to share "across multiple page rendering components" the design dialog will only help if the page share the same rendering component.
If you want to have the header component displayed in a page and all its subpages, then you should use iparsys.
If you just want to reuse the properties of that header component, then it needs to have a fixed path (cq:include in a page component) and then you can reference the properties you need in other page rendering components. I would not suggest that approach since it breaks the idea of having a component. Everything becomes tightly coupled.
What you could also do is save those properties at the page level (some top parent page) and then use InheritanceValueMap in the subpages to read those properties.