In such a confusing situation, with which registrar should businesses register their Chinese character domain name?

As long as this confusing situation remains, clearly the safest route is to register your CCDN with all three registrars. At present, CINIC is the only administrator that is approved by the Ministry of the Information Industry (MII) for CCDN registration within the PRC. It is therefore advisable to register your CCDN with CINIC if you intend to or are doing business within the PRC.