This doesn't quite answer your specific question, but it might help anyway.
Normally when I've done SSL sites, which also haven't had local sandboxes serving SSL, I just use the config file to set the base URL and site URL conditionally with or without the https.
Focus Lab's Master Config already does this automatically. (excerpted below)
$protocol = (isset($_SERVER['HTTPS']) && $_SERVER['HTTPS'] == 'on') ? 'https://' : 'http://';
$base_url = $protocol . $_SERVER['HTTP_HOST'];
$base_path = $_SERVER['DOCUMENT_ROOT'];
$system_folder = APPPATH . '../';
$images_folder = 'images';
$images_path = $base_path . '/' . $images_folder;
$images_url = $base_url . '/' . $images_folder;
$env_config['index_page'] = '';
$env_config['site_index'] = '';
$env_config['base_url'] = $base_url . '/';
$env_config['site_url'] = $env_config['base_url'];
$env_config['cp_url'] = $env_config['base_url'] . 'admin.php';
$env_config['theme_folder_path'] = $base_path . '/themes/';
$env_config['theme_folder_url'] = $base_url . '/themes/';
$env_config['emoticon_path'] = $images_url . '/smileys/';
$env_config['emoticon_url'] = $images_url . '/smileys/';
$env_config['captcha_path'] = $images_path . '/captchas/';
$env_config['captcha_url'] = $images_url . '/captchas/';
$env_config['avatar_path'] = $images_path . '/avatars/';
$env_config['avatar_url'] = $images_url . '/avatars/';
$env_config['photo_path'] = $images_path . '/member_photos/';
$env_config['photo_url'] = $images_url . '/member_photos/';
$env_config['sig_img_path'] = $images_path . '/signature_attachments/';
$env_config['sig_img_url'] = $images_url . '/signature_attachments/';
$env_config['prv_msg_upload_path'] = $images_path . '/pm_attachments/';
With something like this in place, you don't have to worry about relative paths, since the base path used for all path variables will include the correct protocol.