You could try the following wp-config.php setup – note WP writes to the file wp-content/debug.log – this config also stops any errors from being rendered to the browser.
Note that setting the constant WP_DISABLE_FATAL_ERROR_HANDLER to true
enables you to disabled the default WP error screen.
// Disable display of errors and warnings
@ini_set('display_errors',0);
define( 'WP_DEBUG_LOG', true );
define( 'WP_DEBUG', true );
define( 'WP_DEBUG_DISPLAY', false );
define( 'SCRIPT_DEBUG', false );
// disable WP fail-safe screen ##
define( 'WP_DISABLE_FATAL_ERROR_HANDLER', true );