I think this is a good solution. It's simpler, but that usually means better. You could still set up multiple monitors, but now they'd run independant of each other. They could send out an email saying, "Alert: Target 1 Unreachable" and if you receive more than one email then you can be pretty sure there is a problem.

You probably already know this, but the simplest way to retrieve information from a URL is like this:

use LWP::Simple;
$url = 'http://www.google.com';
my $page = get $url;