To avoid corrupting mysql, I'd also change the filenames for mysql before reinstalling it in a subdirectory. You do this in the config.php file.
If I recall correctly, wordpress uses .htaccess to redirect browsers from index.html to index.php, which is why your index.html disappeared -- I don't believe it overwrote it. You may also be able to edit the .htaccess file to remove this line, but I'm not sure what the secondary effects may be if you do this because I've not worked with the latest version of wordpress. Plus having both an index.html and index.php file may (or may not) confuse searchbots indexing your site.
Better to delete it and reinstall it in a subdirectory.
Leva