SwingWorker + JOptionPane [Resolvido]

Nada como ler de novo a API…

protected void process
Receives data chunks from the publish method asynchronously on the Event Dispatch Thread.

protected final void publish
Sends data chunks to the SwingWorker.process method. This method is to be used from inside the doInBackground method to deliver intermediate results for processing on the Event Dispatch Thread inside the process method.
Because the process method is invoked asynchronously on the Event Dispatch Thread multiple invocations to the publish method might occur before the process method is executed. For performance purposes all these invocations are coalesced into one invocation with concatenated arguments.

Ou seja, no meu método doInBackground, tenho que chamar publish, que por sua vez vai chamar process que pode interagir com a GUI.

Alguns links interessantes:

http://enos.itcollege.ee/~jpoial/docs/tutorial/uiswing/misc/threads.html#SwingWorker
http://download.oracle.com/javase/tutorial/uiswing/concurrency/interim.html