... Having come to the conclusion that that my script cannot depend on the server admins keeping the server clock set right,...

If time is such an important issue, it might be so for much more than your script... Don't let your admins get away: having a correct time on a server and keeping it in sync with the Network time is important.

Being insistent on that, you might do a Good Thing for your other scripts, other customers scripts, your company, other users of that server, etc. Definitely persuade them to keep a good time on the server, even if you get a solution for your self as quick as writing a few lines of code.

Use Net::NTP rather for sending your admin a mail as soon as the server's time is more then a few seconds away from the reference time :)