The Total "header builder" function replaces the entire header function as it's more efficient this way, but if you want you can actually use a little code to insert a custom template to be used as your header which would be visible on desktop only and then have the default theme header visible on mobile.
Important Notice: If you need this header to be sticky then you would have to actually use wpex_hook_header_top instead of wpex_hook_header_before in the first function. And then remove the second function and instead use CSS to hide the "#site-header-inner" element on desktops as there isn't a filter you can use to tweak the header-inner classes at this time.
// Add custom header above default header
add_action( 'wpex_hook_header_before', function() {
$template_id = 6874; // replace this with your header template
echo '<div class="hide-at-mm-breakpoint clr">' . do_shortcode( '[templatera id="' . $template_id . '"]' ) . '</div>';
}, 5 );
// Alter default header classes so it displays on mobile only
add_filter( 'wpex_header_classes', function( $classes ) {
$classes[] = 'show-at-mm-breakpoint';
return $classes;
} );