I have a working solution now, however I welcome recommendations...
I have created two RuntimeStore objects, one String to contain all the messages, and one RichTextField to indicate if the window is visible.
1) In the constructor for the display, I create the RTF object and populate it with the String contents.
2) In the onClose() function I remove the RTF from the RuntimeStore.
3) In the the DebugMessage function, I add the message to the String, and if the RTF object exists, then the window is created, so I add the new string to it. Otherwise, the debug window is not open so I don't need to worry.
I realize that this is pretty shabby coding, but it works. Any suggestions for improvement?