Residence Permit and Work Permit dates do not overlap

In a couple of months, my Residence permit will expire, 19 days before my work permit, and contract. I have been told by employer it is not possible to extend residence permit for a short time (I am planning on going back to UK). The local PSB, have also said it is difficult, but that I can be changed to a tourist visa, while still having a work permit, and would be able to stay in China for 30 days after issuance.

Seems a bit dodgy, as I will be working on a L type, but with valid work type.