So, the behavior you describe as problematic is actually the behavior I'd expect - since the data type is string, in a text box control, you can't set the format desired (like you can in the date picker control). If you change those text boxes to calculated values (expression boxes), you'd be able to set the format. The XML is going to store the date value as yyyy-mm-dd - that's displayed in the top portion of the screen shot I've attached.
I saved the form as source files and looked at one of controls in one of the views that is displaying the data as a formatted date - it is odd, it has an xd:datafmt attribute on it - which I would not expect, since on the control, the Format button is disabled.
You could manually modify the veiw to include the attribute on the text box controls you wish to have formatted like this - but really, why not just change the field to a date data type? Then you could format the text boxes as desired?