The issue is that you’re embedding a form within a form … the entry list and single entry are wrapped in a form that is used by Connections.
I think … the simple solution would be to instruct the template to close the form sooner, that you the CF7 form is not wrapped in a form.
excerpt-plus.php file try changing this line:
add_action( 'cn_action_list_after-' . self::$template->getSlug() , array( __CLASS__, 'formClose'), 11 );
add_action( 'cn_action_list_before-' . self::$template->getSlug() , array( __CLASS__, 'formClose'), 99 );
Now, you will either have to move the pagination control to the top of the list OR just hide the input box using CSS. The reason is because this input would not longer be within the Connections form and would no longer work, but the next/previous links will still work fine.
Hope that helps, let me know.