Aside from the form fields, I've tried using these vars with no success:
$form_id = 1;
$unit_tag = 'wpcf7-f' . $form_id . '-p' . url_to_postid(get_option('siteurl')) . '-o1';
echo '_wpcf7='.$form_id.'&_wpcf7_unit_tag='.$unit_tag.'&_wpcf7_is_ajax_call=1';
Am I missing something?