The following modification of your my_crc function produces the same CRC 32 as String::CRC32.

sub my_crc {
    # Within each byte the bits are read LSB to MSB
    # A quirk of Ethernet CRC32
    foreach (@msg) {
        push(@bin_msg, reverse split(//, sprintf('%08b', ord($_))));
    }

    # Augment the message buffer so all message bits
    # will be shifted out of the remainder
    push(@bin_msg, (0)x32);

    # Invert the first 32 bits of the augmented buffer
    # Another quirk of the Ethernet CRC 32
    $bin_msg[$_] ^= 1 for(0..31);

    print "\n";

    while (@bin_msg) {
        my $bit = shift(@bin_msg);
        print "bit: $bit\t\t";
        push(@crc, $bit);

        # shift the remainder and subtract the generator if
        # the bit shifted off was a 1
        if (shift(@crc) == 1) {
            for (my $i = 0; $i < 32; $i++) {
                if ($gen[$i] == 1) { $crc[$i] ^= 1; }
            }
        }
        print @crc, "\n";
    }

    # Reverse the remainder: another quirk of Ethernet CRC32
    @crc = reverse @crc;

    # Invert the remainder: another quirk of Ethernet CRC32
    $crc[$_] ^= 1 for(0..31);
}
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