I would probably install WordPress in a folder, block search engine access to it (for duplicate content issues) and transfer all pages and solve template/theme issues. Then I would get rid of Joomla and all its traces and simply copy index.php and .htaccess from WP folder to root directory.
It's only a suggestion, I can't know what exactly you are doing. Nor I am familiar with Joomla. But WordPress can be installed in a folder and then if you just copy index.php and .htaccess to root folder it will work. It's also a good security practice.
And don't forget to unblock search engines at the end if you follow this suggestion.