Thank you everyone for the help so far. Unfortunately, it's not working properly. Here is my code now:

    my $log = $provoutfile;
    print "Now Processing $log....\n";
    open LOG, "$log" or die "LOG $log: $!\n";

    $linecnt = 0;
    while (<LOG>) {
        chomp $_;
        $linecnt++;

        my @sortedlines = map { $_->[0] } sort { $a->[1] <=> $b->[1] }
        map { [$_, Time::Piece->strptime($_, '%a %b %d %H:%M:%S %Y')->
+epoch ] } @lines;
        $line = "";
        $linecnt = 0;
     }
[download]

It doesn't fail or error or anything... it just doesn't sort properly. When I grep TIMESTAMP out of my output file, the last dozen-ish lines look like this:

TIMESTAMP=Fri Nov  2 16:33:18 2018
TIMESTAMP=Fri Nov  2 17:26:35 2018
TIMESTAMP=Fri Nov  2 17:26:35 2018
TIMESTAMP=Fri Nov  2 17:27:33 2018
TIMESTAMP=Fri Nov  2 17:27:33 2018
TIMESTAMP=Thu Oct 18 18:29:15 2018
TIMESTAMP=Thu Oct 18 18:29:15 2018
TIMESTAMP=Thu Oct 18 18:29:27 2018
TIMESTAMP=Thu Oct 18 18:29:27 2018
TIMESTAMP=Thu Oct 18 19:06:32 2018
TIMESTAMP=Thu Oct 18 19:06:32 2018
[download]

Maybe it's because each individual log entry is broken up by newlines?