I would create a GPO (or edit an existing one) that would stop the automatic reboot due to to updates and use the
gpupdate /force command on each of the servers.
The option to set this can be found in Computer Configuration > Administrative Templates > Windows Components > Windows Update. You'll still get the annoying prompt to reboot the machine, however there won't be a countdown. It's called "No auto-restart for scheduled automatic updates installations"
If the shutdown timer starts you can use the
shutdown -a command which should abort the reboot procedure.