I'd guess that problem might go away if you make their bonuses contingent on a sleep numbers (along with the SLAs) for whoever has to run the application or it's downstreams whether that's a dev or an ops type. Base the number on pagerduty calls or something like so they can't game the number.

That is a wonderful idea. Managers are responsible for the performance of their teams. NOBODY wants to sandbag sleep numbers, so it'd be a decent comp metric.