other portlets running in the portal at the same time
Regardless of the scope, portlets from separate war files will never be able to share PortletSession data. The APPLICATION_SCOPE of the PortletSession only mitigates the sharing of data between portlets packaged within a common web application archive.
For true global information sharing, you need to create some kind of Portlet Service, Web Service, or commonly accessible database table.
-Cameron McKenzie