How can I programmatically bring up the document properties window in Word and go to the Summary tab?

You can bring up a seperate box for this (works in both Word 2000, 2003, 2007 and 2010):

Application.Dialogs(wdDialogFileSummaryInfo).Display

or

Application.Dialogs(86).Display

You can also program against this dialog. See here for an example.