Accessing html.tpl.php variables from outside
Direct answer to your question - you can populate the variables you need by emulating the same functions that the processing function for html.tpl.php uses to render the page:

http://api.drupal.org/api/drupal/includes%21theme.inc/function/template_process_html/7

function template_process_html(&amp;$variables) {
  // Render page_top and page_bottom into top level variables.
  $variables['page_top'] = drupal_render($variables['page']['page_top']);
  $variables['page_bottom'] = drupal_render($variables['page']['page_bottom']);
  // Place the rendered HTML for the page body into a top level variable.
  $variables['page']              = $variables['page']['#children'];
  $variables['page_bottom'] .= drupal_get_js('footer');

  $variables['head']    = drupal_get_html_head();
  $variables['css']     = drupal_add_css();
  $variables['styles']  = drupal_get_css();
  $variables['scripts'] = drupal_get_js();
}


So to access the styles variable, you would just need to call the same function the template engine is using:

$mystyles = drupal_get_css();


However - just to check, these values are already on your page because the html.tpl file is a wrapper for page.tpl.php. Sure you want to print it twice?