Per SOL4186 I don't think you'll be able to use a null in the send or receive string:
"Note: The BIG-IP system does not allow the ASCII character 0 (NUL)."
I tried adding this in both \x00 and \x000 format through the GUI, the CLI and the bigip.conf file but all attempts resulted in the 'embedded zero' error.
You could either check with F5 Support on why this restriction is in place or use an external monitor to send the null. A standard TCP monitor would be simpler and more efficient, so it might be worth checking with F5 on this.
Aaron