One change which I would make would be the following which implements a variable sleep such that the sending of mail is more evenly timed to match 15 second intervals - I have used something similar for a dispatch of mail to our (many thousand) local users in order to stagger the load on the mail server.

eval "use Time::HiRes qw( time sleep )";

foreach (@{ $userinfo }) {

    my $time = time();

    ...

    sleep 15 - ((time() - $time) % 15);
}
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However, if you are employing sendmail as a local MTA, you may be interested in taking a look at vthrottle which is a rate throttling mechanism for Sendmail implemented via the milter interface (which can also be interfaced in Perl by way of Sendmail::Milter or PMilter). This may constitute a longer term solution for your mail throttling.