Hi Will,
If the automatic override does not work in that section, then the theme is probably using a hard-coded search box instead of the get_search_form hook. Pop-up, pop-out and similar interactive search bars are usually hard-coded for a reason – probably because an override would break the functionality.
You might have to ask the theme author, if there is any way to replace it programmatically, without loosing the pop-up functionality. Then the original search form can be replaced within the theme files (or via custom hook) witht the plugin shortcode.