Hi Geoff,

The only time I've been involved in something like this the sites were using Shibboleth as the single sign on (SSO) authentiator. LDAP most likely could also be used as a middle SSO component between the two. Though LDAP or Shibboleth might be too complex for your needs.

However there do seem to be lots of articles online about integrating Wordpress and Moodle so maybe one of those links will point you in the right direction, if you search on Google for "wordpress moodle SSO" there seem to be a variety of options e.g.

http://blog.giuseppeurso.net/moodle-and-wordpress-single-sign-on-in-20-minutes-part-1/