There are several points here which can cause the OP difficulties.

The first is he is not moving province, not even city. This can be problematic if for example the bosses of one school don't like the other, they or rivals or simply don't want to co-operate. The fact you are leaving or have left will have caused them to lose face and rubbing their noses in it by moving to a new school who could be a rival down the road won't help you at all.

The second is that FAO's generally don't tread on each others toes, they have their own patches and tend to stay within the boundaries. If they are good friends your leaving might be ignored at the expense of a lavish dinner. If not there is another problem to work with.

Regarding cancellation of the FEC, certainly that needs to be done. Once you have an active one in the computer you can't have one elsewhere in China. Simple as that. You can either let it expire naturally or ask for it to be cancelled. It is literally the click of a few buttons to cancel it online so that enables you to begin a new application but if they are pissed at you don't expect them to do it any time soon. As for cancelling it yourself, even if you had the document or a copy, negotiating the SAFEA office is a minefield and they will always side with the school, by the time you might eventually get it cancelled it would probably have cancelled itself out anyway.

The release letter is a definite requirement now so long as you have an active RP or FEC. If you are starting the process again you don't need it.

I have noticed things are being a lot more coordinated this year and much more information is being shared between provinces whereas previously it wasn't.

It maybe here that money will solve the problem whether from you or your new school. If they want you badly they may just pay it.