Allow asynchronous logging via Loggly, Papertrail, or Splunk
Allow asynchronous (fast, non-blocking) logging via syslog daemon.
You don't even need to make it a 1-click installation for Loggly, Papertrail, or Splunk.
Just allow us to use the syslog daemon and then we can follow instructions at https://www.loggly.com/docs/php-logs/ or http://help.papertrailapp.com/kb/configuration/configuring-centralized-logging-from-php-apps/ or wherever.
Those instructions say they'd require root access (which Cloudways customers don't have), but it wouldn't require root access if you did the first steps for us.