The munchkin code is added via admin/advanced/tracking & analytics using custom code/all pages. Do you think I could add the munchkin code to the embed contact form code?
The other way around.
The Munchkin embed block is going where you want it to go (directly in the outer document HTML). The form is being wrapped in an inaccessible IFRAME (inner document).
If you don't want to have to hack together communication between the inner and outer document, then you have to get the form in the outer document (which is, of course, how the embed code is supposed to work and how it functions on a vanilla HTML page).