The Police Clearance will also take up to a month.

Exactly right. In the UK about 40 days, although I suspect a month is enough. Problem is you really need to go back home and do it, you can't even get a friend or relative to send a scanned copy. I suspect you are right about the weeding out of those who don't want to return home or don't have the funds to do so. I'm still curious as to your mysterious visa status, are you a HKID holder and so does that grant you longer visa time in China?