I don't know if that's at all possible. AFAIK, $! is magic, in the sense of internal perl magic.
You can try to work around with ^H. If your error messages are not meant for anything but displaying on a terminal, you can append a series of ^H after your digit to overwrite it, then the message, which won't change the numeric value. Not really helpfull in a log file, but it works on a term:
$error = "2\x08message";
print $error+0 . "\n";
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