Let's look through your script one line at a time.
var myStories = myDocument.textFrames[myCounter].parentStory;
The trouble with this line is that if your document contains any linked text frames, you'll end up exporting the story multiple times. Instead, you should iterate through stories, as shown in the ExportAllStories example script.
Where did this come from? In the first line, you create a reference to a story. If you look at the object model viewer listing of the properties of a story, do you see textExportPreferences? No. TextExportPreferences exist at the application and document level, but not on a story. You want app.documents.item(0).textExportPreferences.