So the problematic block of lines start with set private ", then some junk that doesn't containt quotes and then it ends with a quote, right?

You seem to be parsing this line-by-line, correct? So, modifying your code to make a very rudimentary state machine, i'd guess something like this would do:

my $isprivatekey = 0;
for my $line (@diff) {
    if($isprivatekey) {
        if($line =~ /\"/) {
            # last line of private key
            $isprivatekey = 0;
        }
        next;
    }
    if($line =~ /set\ private\-key/) {
        # uh, get some useless stuff here
        $isprivatekey = 1;
        next;
    }

    next LINE if $line =~ /set password ENC/;
    [...]
}
[download]

This should skip the whole private key block altogether