Did you try app.ProjectClosed?
PublicWithEvents app as ViewDraw.Application
PublicSub app_ProjectClosed() Handles app.ProjectClosed
Debug.Print("Project has been closed.")
EndSub
This is different, as you noted, from closing down the entire DxDesigner main window. That fires app.Shutdown, as in:
PublicSub app_Shutdown() Handles app.Shutdown
Debug.Print("app shutdown")
EndSub
I tested both of these and they work as expected.