show() is one of the few methods that need not be called from the EDT.
In fact, when you first call it, you don't have an EDT, you call it
from the main thread.

You even have the code in front of you, and you claim this? There is no
new EDT started. The eventpump is replaced.

Here are some code snipplets that can give a clue how to do event pumping
yourself while your dispatching thread is stuck waiting for some long
operation:
This function gives you the event despatching queue of the system:

private EventQueue getEventQueue()
   {
       return (EventQueue)AccessController.doPrivileged(new
PrivilegedAction()
       {
           public Object run()
           {
               return Toolkit.getDefaultToolkit().getSystemEventQueue();
           }
       });
   }

// This function pumps events on the queue until the receiverThread
returns
   private void pumpEvents(EventQueue queue, Thread receiverThread) {
        while (true) {
               if (receiverThread.isAlive() == false) {
                   break;
               }
               pumpEvent(queue);   // pump event (may be blocking but
receiverThread sends empty event when finished)
        }
   }
   
   
   private void pumpEvent(EventQueue queue) {
       try {
           AWTEvent event = queue.getNextEvent();  // may be blocking if
no events
           dispatchEvent(queue, event);
       } catch (InterruptedException e) {}
         catch (Throwable x) {
             handleThrowable(x);
       }
   }

/**
   * Copy/Paste of the Sun's JDK 1.3 implementation in
java.awt.EventQueue.dispatchEvent(AWTEvent)
   * @param queue The system EventQueue
   * @param event The event to dispatch
   */
   protected void dispatchEvent(EventQueue queue, AWTEvent event)
   {
       Object source = event.getSource();

       if (event instanceof ActiveEvent)
           ((ActiveEvent)event).dispatch();
       else if (source instanceof Component)
           ((Component)source).dispatchEvent(event);
       else if (source instanceof MenuComponent)
           ((MenuComponent)source).dispatchEvent(event);
       else
           System.err.println("[Communication] Unable to dispatch event "
+ event);
   }

   /**
   * Handle a RuntimeException or Error happened during event
dispatching.
   * If the system property <code>sun.awt.exception.handler</code> is
defined,
   * that handler will be used, otherwise it simply logs on
<code>System.err</code>.
   */
   protected void handleThrowable(Throwable x)
   {
       String handlerName = (String)AccessController.doPrivileged(new
PrivilegedAction()
       {
           public Object run()
           {
           return System.getProperty("sun.awt.exception.handler");
           }
       });

       if (handlerName != null)
       {
           try
           {
               Object handler =
Thread.currentThread().getContextClassLoader().loadClass(handlerName).newInstance();
               Method handle = handler.getClass().getMethod("handle", new
Class[]{Throwable.class});
               handle.invoke(handler, new Object[]{x});
               return;
           }
           catch (Throwable ignored)
           {
               System.err.println("[Communication] Exception occurred
while invoking AWT exception handler: " + ignored);
               // Fall through
           }
       }

       System.err.println("[JDK13QueueEventPump] Exception occurred
during event dispatching:");
       x.printStackTrace();
   }

to send empty event when receiver thread is finished use there:
           // send empty event to ensure that pumpEvent returns. sleep
added in order to give this thread time to exit
               javax.swing.SwingUtilities.invokeLater(new Runnable(){
                   public void run() {
                   }
               });

Here are some code snipplets that can give a clue how to do event pumping
yourself while your dispatching thread is stuck waiting for some long
operation:
This function gives you the event despatching queue of the system:

private EventQueue getEventQueue()
   {
       return (EventQueue)AccessController.doPrivileged(new
PrivilegedAction()
       {
           public Object run()
           {
               return Toolkit.getDefaultToolkit().getSystemEventQueue();
           }
       });
   }

// This function pumps events on the queue until the receiverThread
returns
   private void pumpEvents(EventQueue queue, Thread receiverThread) {
        while (true) {
               if (receiverThread.isAlive() == false) {
                   break;
               }
               pumpEvent(queue);   // pump event (may be blocking but
receiverThread sends empty event when finished)
        }
   }
   
   
   private void pumpEvent(EventQueue queue) {
       try {
           AWTEvent event = queue.getNextEvent();  // may be blocking if
no events
           dispatchEvent(queue, event);
       } catch (InterruptedException e) {}
         catch (Throwable x) {
             handleThrowable(x);
       }
   }

/**
   * Copy/Paste of the Sun's JDK 1.3 implementation in
java.awt.EventQueue.dispatchEvent(AWTEvent)
   * @param queue The system EventQueue
   * @param event The event to dispatch
   */
   protected void dispatchEvent(EventQueue queue, AWTEvent event)
   {
       Object source = event.getSource();

       if (event instanceof ActiveEvent)
           ((ActiveEvent)event).dispatch();
       else if (source instanceof Component)
           ((Component)source).dispatchEvent(event);
       else if (source instanceof MenuComponent)
           ((MenuComponent)source).dispatchEvent(event);
       else
           System.err.println("[Communication] Unable to dispatch event "
+ event);
   }

   /**
   * Handle a RuntimeException or Error happened during event
dispatching.
   * If the system property <code>sun.awt.exception.handler</code> is
defined,
   * that handler will be used, otherwise it simply logs on
<code>System.err</code>.
   */
   protected void handleThrowable(Throwable x)
   {
       String handlerName = (String)AccessController.doPrivileged(new
PrivilegedAction()
       {
           public Object run()
           {
           return System.getProperty("sun.awt.exception.handler");
           }
       });

       if (handlerName != null)
       {
           try
           {
               Object handler =
Thread.currentThread().getContextClassLoader().loadClass(handlerName).newInstance();
               Method handle = handler.getClass().getMethod("handle", new
Class[]{Throwable.class});
               handle.invoke(handler, new Object[]{x});
               return;
           }
           catch (Throwable ignored)
           {
               System.err.println("[Communication] Exception occurred
while invoking AWT exception handler: " + ignored);
               // Fall through
           }
       }

       System.err.println("[JDK13QueueEventPump] Exception occurred
during event dispatching:");
       x.printStackTrace();
   }

to send empty event when receiver thread is finished use there:
           // send empty event to ensure that pumpEvent returns. sleep
added in order to give this thread time to exit
               javax.swing.SwingUtilities.invokeLater(new Runnable(){
                   public void run() {
                   }
               });