So after a few days of back and forth with support, I may have finally received some insight as to why the server keeps randomly rebooting. Apparently, their crappy datacenter monitoring keeps triggering ping loss alerts, so they send an engineer over to physically reboot the server every time. I was not aware that this was the default monitoring option on their current server lines, and have disabled it so this should avoid forced reboots going forward.
I am standing up a basic ping monitor to alert me via email and SMS if the server actually goes down, and can quickly reboot it myself if ever needed (may even write some script to reboot via API if x concurrent ping fails, or something). Full monitoring stack is still in progress but not truly necessary to ensure stability at the moment.