Here are variations I've tried in the child now which did not work:
If I understand you correctly, do the following:
(1) Add an input of type "hidden" to your form.
(2) Add to, or create, an 'onsubmit' event to that form
(3) on submit, access the element from the iframe and extract its value
(4) put the value inside the hidden input
(5) have onsubmit return "true"