With the moved core, you want exactly this in the first line of the config.core.php files (as you have above) and it should also be the first thing in config.inc.php:
define('MODX_CORE_PATH', '/var/www/sites/blah.com/core/');
You need it there, even though it's defined in config.core.php because sometimes a script might go directly to the config.inc.php file.
MODX uses the config.core.php files just to find the config.inc.php file. Once it finds config.inc.php, it gets all the other locations from there.
Remember that when you move the core, you also move the connectors and processors directories because they're under the core. So these would make sense with your moved core:
define('MODX_CONNECTORS_PATH', '/var/www/sites/blah.com/core/connectors/');
define('MODX_PROCESSORS_PATH', '/var/www/sites/blah.com/core/model/modx/processors/');
Setup tends to daisy chain the settings like this:
define('MODX_CONNECTORS_PATH', $corePath . 'connectors/');
But on some servers, you need to hard code each path on its own.