Moving CiviCRM Into its Own Subdomain to Create a Drupal Multisite

I had CiviCRM installed and working as a module on the main Drupal 6 site. For better site performance I decided to move the CiviCRM module into a subdomain of the site. This way the CiviCRM modules would not slow the main site when they are not needed, and the main site's modules would not slow the CiviCRM modules when the main site's modules are not needed. I still wanted a shared database including the user profiles. I also wanted a shared login so that a user who has permission to access CiviCRM who is logged into the main site would have access to the CiviCRM's subdomain without having to login again.

I left the modules that depend on both the main site and CiviCRM in sites/all/modules/contrib. I moved all modules that have no CiviCRM dependency from sites/all/modules/contrib to /sites/www.example.com/modules/contrib. l moved all modules that depend only on CiviCRM from sites/all/contrib to /sites/civicrm.example.com/modules/contrib. The entire civicrm directory was moved from sites/all/modules/ to /sites/civicrm.example.com/modules/.

The dependencies were determined by looking at http://www.example.com/admin/build/modules. In directory /sites/all/modules/contrib I have modules cmf, menu_breadcrumb, menu_node, rules, webform.
jquerymenu, menu_editor and menu_node_edit, views. In /sites/civicrm.example.com/modules/contrib I have only the module cd_sunlight.

I moved civicrm.settings.php from /sites/default to /sites/civicrm.example.com/. In this file I edited the values $civicrm_root to the new path. Also the CIVICRM_UF_BASEURL define statement was edited to be: define( 'CIVICRM_UF_BASEURL' , 'http://civicrm.example.com/' );

I made changes to the server configuration so http://civicrm.example.com/ points to the same directory as http://www.example.com/ does. Then I ran http://www.example.com/update.php.

Site performance at http://www.example.info improved as expected. But there is trouble at http://civicrm.example.info. I have missed something because at http://civicrm.example.com/admin/build/modules I do not see any CiviCRM modules nor do I see cd_sunlight. So I cannot enable them and they do not appear in the menu. All the modules in /sites/all/modules/contrib do appear there though.

In sites/default/settings.php I had set $base_url=http://www.example.info. I tried commenting this line out to leave $base_url undefined. The only difference this made is I had to login at http://civicrm.example.info when I was already logged in at http://www.example.info. The expected modules still did not appear at http://civicrm.example.com/admin/build/modules.

I need help to make this work as intended so CiviCRM is available at http://civicrm.example.com.