Your moniker suggests you like doing odd jobs.

Of course, you are not permitted to take a paid teaching job with your RP as it is not linked to a Z visa. Your initial RP will likely be of 180 days' duration even though you may have applied for one of 360 days or 720 days. If you leave the area of your RP to reside somewhere else overnight, you must register there with the local PSB within 24 hours of your arrival to avoid the possibility of a 2,000 RMB fine. if you aren't staying at a hotel.

This enforced 2-week interview routine seems very strange.

Peruse the 'Know Your Rights' section for more information.

Yes I know I won't be allowed to work. What I want to know is will I be able to up sticks and move to a different town/city in the same province and keep the same residence permit taking into account that I would need to register at a police station/PSB in that different place?