How would we limit the drop down for the Date's Timzone field?
The Date module's field elements are supplied by the Date API module. The timezone component is supplied by its process callback date_timezone_element_process(). 

It triggers hook_date_timezone_process_alter() which can be evoked by a custom module to alter the options within $element['timezone']['#options'].

For example:

/**
 * Implements hook_date_timezone_process_alter().
 */
function MYMODULE_date_timezone_process_alter(&amp;$element, &amp;$form_state, &amp;$context) {

  if (isset($element['timezone']['#options'])) {
    // @TODO: Supply an array filter function that filters
    // IANA TZ names that don't correspond to
    // UTC - PST/PDT - MST/MDT - EST/EDT - GMT

    // Example: Filter TZ's that are only in the Americas
    $element['timezone']['#options'] = array_filter($element['timezone']['#options'], function($key) {
      return strpos($key, 'America/') !== FALSE;
    }, ARRAY_FILTER_USE_KEY);

  }
}