Your hypotheses is that read did a partial read and needs to be called again to get the rest. You've offered no proof of this at all, so let's verify it.

Does adding the following to your script help?

use CGI 3.55;
BEGIN {
    *CGI::read_from_client = sub {
        my($self, $buff, $len, $offset) = @_;
        local $^W=0;                # prevent a warning
        die if $MOD_PERL;
        while ($len) {
            my $bytes_read = read(\*STDIN, $$buff, $len, $offset);
            die "read: $!\n" if !defined($bytes_read);
            last if !$bytes_read;
            $len    -= $bytes_read;
            $offset += $bytes_read;
        }
    };
}
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help?