Apparently the Engineer before me battled updates for MONTHS before giving up and just leaving it for someone else to inherit. That said, I have fixed my problem. I didn't have to disable anything, or uninstall anything.
I had to modify a registry setting that allowed the TrustedInstaller more time to do its work.
HKLM\SYSTEM\CurrentControlSet\Services\TrustedInstaller
Inside that key is a REG_DWORD named "BlockTimeIncrement" and it's default value is Decimal 900 - so 15 minutes. And it apparently kept timing out. If you change that value to something higher, I changed it to 10800 (hex is 2a30) which is 3 hours, and within about 25 minutes the server patched, rebooted, and came back up successfully.
It is now fully up to date and working fine. Just a heads up for anyone with similar issues.