Heading South Towards Natal
We tried to take the state highway but all the petrol stations were empty, and the few cars on the road were not going far, I recommend using the national BR116. After the BR116 reconnects with the state highway it gets much better and there are many large petrol stations with lots of cars.
Heading West Towards Jericoacoara, Piauí, and Maranhão
Take a bus out to Caucaia on the outskirts of the city from the center (ask the bus driver). There's a gas station at a roundabout where the C-085 is leaving town. It seems like people shouldn't really be able to stop there, but there's plenty of people who are willing to stop. Lots of people are going to beaches along the way... I even got someone going all the way to São Luís in Maranhão.