I know what you mean. I am going through the same performance.

I am not Irish but from England. I am also in Nanjing and I am simply moving from a university to a public school less than an hour away and have been told the same thing.

I had already got my degree authenticated but this CRB check is a ballache to do. A similar rule seems to apply in England now. You have to front up in person a the police station first, then they send it off to somewhere else who then will only send it to an address in the UK.

It looks like I'm going to have to bite the bullet and fork out for a ticket home and waste time which I had already planned this summer.

I too was offered a job in Chengdu and they said they only need the authentication for new applications, not transfers or renewals. The whole system seems to be a shambles at the moment. If I can negotiate with them for a higher salary I am simply tempted to take that job instead.