The php.ini file is not recursive and will likely not be affecting your settings in directories deeper down. Setting the mode to PHP5 (Single php.ini) through the PHP Config icon in the cPanel may help. You can also do the following which should most definitely work for you.
Have bluehost enable shell access for you, then login through ssh and run the following:
mysqldump -u dbprefix_username -p dbprefix_database > dbbackup.sql
Replace dbprefix_username with the actual username for your database and replace dbprefix_database with your actual database name. Keep your wp-config.php file open in another window so you can enter the database password when it prompts you for it.
Using this method will not run into any timeout problems.
Repair and optimize your databases before doing the export just in case some corruption is interfering with it: