Just send a cross-domain XHR request with the data from the form instead of submitting the form. CORS is only for the former.
If you must do it the other way, negotiate with the frame using postMessage.
And since the contents of the IFRAME is an XML document, there is no JavaScript code inside the IFRAME which could make use of postMessage or something.
How does that stop you? Include a script element under the HTML or SVG namespace (<script xmlns="http://www.w3.org/1999/xhtml" type="application/ecmascript" src="https://stackoverflow.com/questions/6718664/..."/>) anywhere in the XML.