Well, my answer will probably not make you fully happy. But at least you can use a CMS page after this change. It will take up much more changes to be able to only enable a single CMS page.
The WebsiteRestriction module uses the full action name of a page to determine whether the visitor is allowed to view the page. The logic to determine this can be found in
Enterprise_WebsiteRestriction/Model/Observer.php in the method
restrictWebsite. Since the full action name contains the module, controller and action name there is no difference between the CMS pages. All pages react to the full action
By default CMS pages, as you noticed, are not visisble when running in restriction mode. You can change this by adding the
cms_page_view node to the the following XML xpath
frontend/enterprise/websiterestriction/full_action_names/generic. This will add all CMS pages to the whitelist and make them viewable when not logged in.
The default list of available actions can be found in
Enterprise_WebsiteRestriction/etc/config.xml. I do firmly suggest that you create your own module to add your additional nodes to the XML instead of making changes to the
config.xml of the restriction module.
Hopefully this will help you a bit in the right direction.
If you really want to only make a few CMS pages available then you should extend the the functionality of
Enterprise_WebsiteRestriction/Model/Observer.php and add logic that matches on, for example, CMS page IDs which can be found in the request object. For this however you need some additional Magento experience, but perhaps you already got sufficient Magento time under your belt.