Visa extension will expire before work permit papers

I have a one year extendable (60 day) visitor (student) visa that expired on the 18 but just got extended for one more week, until the 27th. I was studying at TLI but now I will be teaching for them. They have sent my paperwork already to the Ministry of Education. I may not get them back before the 27th. Even if I do, I still have to go to the Ministry of Foreign Affairs (to get my work permit) and give them the paperwork from the Ministry of Education, a certification of employment, and my passport with my visa that expires on that day. (that is if i even get it back before the 27)
After reading all of the horror stories about overstaying visas, do you think it would be wise to get out of Dodge and fly to HK for the day so I could return with a new 30 day landing visa?
Can I still get a work permit and eventually an ARC with a landing visa?
My current visa is a visitor visa, and that would need to be switched in order for me to work anyway, correct?
muchas gracias