So we can now add Shanxi province to the list of places requiring the police check from home. What is confounding me is this: is this now a nationwide thing, or only at the provincial level?

My suggestion for anyone without a homeland police check or unable to get one is to contact one of the China-wide recruiters. A girl will be assigned to you to help you find a suitable job. Stress that you cannot provide nor obtain a homeland police check. Ask her to provide you with a list of all places that don't need a homeland police check, so that you may choose the provinces/autonomous regions/municipalities from that list where you would like to teach. Then she will do the rest. There's no point in her scamming you, as she won't get any commission unless you sign a teaching contract. The Chinese do not like to work for nothing. Do your two-semester gig, then fly home and get your police check done.