Our hosting provider was able to make the upgrades and restart the servers within the first 30 minutes of the delivery window.
We then went over all the applications that run on these servers, and discovered a couple of services that did not start up correctly on their own, and brought them up. These findings will result in tickets to ensure these services are correctly managed.
We also discovered an issue with one server's RAID battery that will also require downtime, we will schedule that and report on it in a new incident.