I've run this through the debugger a few times, without quite figuring out how these parameters are supposed to be passed in, nor why they are missing from $s->{server} where Net::Server::Proto::SSLEAY is expecting them.

That's because the keys SSL_cert_file SSL_key_file are missing from the default structure in sub options from Net/Server.pm line 1338 (as of version 0.99) - it's a bug:

### set up default structure
sub options {
  my $self = shift;
  my $prop = $self->{server};
  my $ref  = shift;

  foreach ( qw(port host proto allow deny cidr_allow cidr_deny) ){
    if (! defined $prop->{$_}) {
      $prop->{$_} = [];
    } elsif (! ref $prop->{$_}) {
      $prop->{$_} = [$prop->{$_}]; # nicely turn us into an arrayref i
+f we aren't one already
    }
    $ref->{$_} = $prop->{$_};
  }

  foreach ( qw(conf_file
               user group chroot log_level
               log_file pid_file background setsid
               listen reverse_lookups
               syslog_logsock syslog_ident
               syslog_logopt syslog_facility
               no_close_by_child
               no_client_stdout tie_client_stdout tied_stdout_callback
+ tied_stdin_callback
               leave_children_open_on_hup
               ) ){
    $ref->{$_} = \$prop->{$_};
  }

}
[download]

Add the keys below leave_children_open_on_hup and presto - it works, at least it doesn't die anymore.

update: I'm not sure whether it's the right place to add those keys, since the machinery of those modules is hard to grasp with little time at hand. Maybe you should file a bug report.