When Toni Epple and I were at Skyguide in Geneva last week, we were shown SEVERAL applications that the Skyguide developers want to port to the NetBeans Platform. Fortunately, one of these is... an open source application! It is called Scrinch, a scrum tool that the Skyguide developers use internally for managing their projects. Get the sources here:
And you can start the application via web start after going to this page:
This is what it looks like:

And here's a quick prototype of the same application ported to the NetBeans Platform:

One of the NetBeans Platform's main advantages is already clear, even in this simple prototype: the window system lets you divide the UI in a much better way than what standard Swing allows. Forget all those JTabbedPanes and use TopComponents instead, which can be opened/closed individually and enable the user to set up a workspace, rather than being locked into the static format of JTabbedPanes.
The above prototype can be created in about an hour or two. The start is to create a new application, wrap the external libraries in library wrapper projects, create a new TopComponent for the main windows in the application, and connect those TopComponents to the existing JPanels (i.e., TopComponent.add(JPanel)). After that, there'd need to be some analysis of how the different parts of the application relate to each other, whether support should include being able to work with multiple Scrinch files, as well as decisions about how to correctly divide the existing JPanels (and other containers) into the NetBeans window system.
Then the actual development could begin... managed in Scrinch, of course!