Remote commands or running scripts on a set of computers based on a script run on another computer

Get #1 to push the reboot status to #2 rather than #2 having to query #1 (since you mentioned permission issues due to SYSTEM context). So one possible solution:

#1. On the servers that have rebooted, perhaps create a scheduled task that dumps a reboot status file to a folder share?

#2. On the servers that need to reboot based on #1, check that folder share.

#3. Grant readonly access to EVERYONE on the folder share, and read/write access to the context under which the scheduled task of #1 runs?

Another approach would be to use Automox API to pass the data around (you could use TAGs).

Just remember that #2 may end up rebooting multiple times unnecessarily if the status of #1 is not updated on-time. For example, #1 has scheduled task to tag itself as needing reboot. This scheduled task runs every 60minutes. If #2 checks #1 every 15 minutes, it would end up rebooting 4 times. This logic shouldn’t be difficult to handle. Easiest way would be to use different time durations e.g. #1 = 15minutes, #2 = #60minutes.