Credit goes to Michelle O'Rorke.  She had blogged about how to do this, but it didn't sink in for me the first time around.  You need to change the field display settings so that Domino will render the date into international format ("yyyy-mm-dd").  When the Dojo control processes the value in the field, it will format the date into the format using the i18n settings it detects in your browser. 

When you submit the form, Domino will be able to process the date because of the display settings for the field.  The only other thing to do is add a computed for display field that will display the date normally ("mm/dd/yyyy" for us Yanks) when a document is being read.  Here's a picture of how to do the date field settings: