With a full AdBlue tank, your car should be good for the next few thousand kilometres at the very least, not just 600km. This makes me think the sensors that measures the contents of the AdBlue tank are telling the car’s computer lies about how full it is.

As you’ve identified, if the computer thinks the AdBLue tank is empty (even if it’s still full) it can refuse to restart the engine. So you need to sort out the sensor and sender units in the AdBlue tank to make sure that the car know it has plenty of AdBlue remaining. This could involve a recalibration or perhaps some new sensors and parts.

In the meantime, I’d keep the AdBlue topped up to full all the time to avoid being stranded with a car that won’t start. Pay attention to the car’s performance, too. In some cases, the computer will first scale back performance if the vehicle is low on AdBlue before it stops the engine altogether. So any unexplained fall off in performance might indicate the vehicle is beginning to think it’s out of AdBlue.