Can stay permit be converted back to residence permit?

Previous employer refuses to give me documents to change to a new school until I cancel my residence permit (RP). Long story. Bad relationship. SAFEA will not do anything.

New school is ready to hire me immediately.

If RP gets canceled, I will need a 30-day stay permit to stay. Can this stay permit be converted back to a residence permit?

What I've heard so far:
1) new company's HR initially said I could convert stay permit back to RP without having to exit. Then a few weeks later they said they spoke to the "government" and were told I needed to exit and get a new Z if my current RP were to be canceled.
2) local foreign expert bureau has repeatedly told me I can apply for a new foreign expert certificate while on a stay permit, and that PSB/immigration/whoever should be willing to convert me back to an RP.
3) today my friend called the exit entry administration bureau at 0512-6660-1111 and was told that I can convert a stay permit back to an RP if I find a new job within 30 days.