> Ideally I'd have it such that once the https session was started, any access to the http site bounced them over to https again, until they logged out.

Maybe it can be done on web server side, but I'm not sure.

> How to redirect logged in users accessing /user/login to specific page?

Don't forget [you can alter][1] any `drupal_goto()` calls:


    /**
     * Implements hook_drupal_goto_alter().
     */
    function YOURMODULE_drupal_goto_alter(&$path, &$options, &$http_response_code) {
      global $user;
    
      if (current_path() == 'user/login' && $path == 'user' && user_is_logged_in()) {
        // Redirect to front page.
        $path = '';
        drupal_set_message(t('Welcome back, %username!', array('%username' => $user->name)));
      }
    }


  [1]: https://api.drupal.org/api/drupal/modules!system!system.api.php/function/hook_drupal_goto_alter/7