Modify (even rename) WP core files is never a good practise.
Try this instead:
Install Wordpress in a phisical subfolder in your site root, (e.g. /WP).
After that, in the .htaccess file in the root folder of your site insert something like this:
RewriteRule blog/(.*) WP/press/$1 [L]
RewriteRule press/(.*) WP/press/$1 [L]
RewriteRule careers/(.*) WP/careers/$1 [L]
RewriteRule anything_here/(.*) WP/anything_here/$1 [L]
Off course, add a rewrite rule for every (virtual) subfolder you want to serve with wordpress.
Virtual subfolders can represent pages, categories or anything else in wordpress.
Don't forget to enable pretty permalinks in wordpress.
In this way only your current application resides in the root folder and everithing is well organized and maintainable.
In this solution, adding a new WP page means add a new .htaccess rule. A workaround is to use a general parent page: create a page named 'Pages' (slug 'pages') then create every other page as a child of this page.
In .htaccess add:
RewriteRule pages/(.*) WP/pages/$1 [L]
now every page that is child (even grandchild) of 'Pages' will be served correctly.