I found the solution — start again! Must have been some issue with the unzipping of the ZIP file. Once I did the following the install under local WAMP was as easy as advertised!
1. redownload the ZIP file
2. extract to a separate directory (important! this is where my problem started)
3. copy the new extraction folder to your wamp/www/ directory
4. start WAMP services
5. edit your wp-config.php then install using http://localhost/wordpress/wp-admin/install.php
