The crank position sensor for the 06 Jetta BRM is part of the rear main seal and is anything but easy to replace. You would have to pull the tranny. The cam position sensor will not stop an engine from running, but may make it hard to start.
If you have access to a VCDS, and there are several around the state, I would check the torsion value, idle compensation. There are some issues with the wiring. For example, if your torsion value is '0' and moving the cam timing makes no difference, you have a bad cam position sensor. I doubt it, as it starts easily cold. There can be hot start issues related to the fuel temp sensor.
The crank sensor is more likely. The plug for the crank sensor is difficult to remove. It is about even with the bottom of the oil filter housing and goes into a hole toward the rear main seal. With the engine running, check to see if there is any movement of the wire that will cause the engine to 'hiccup'.
There are some known grounding issues with the wiring. That can also be a problem. Whenever there are gremlins, I check the grounding acorn nuts by the ECU and under and around the battery. We clean the corrsion and apply an anti-corrosion grease. Once done, that sometimes eliminates 'weird problems'.
Good luck. If you get in a bind, there are several ppl we know in TX and OK