Jetta - Volkswagen :: 2002 TDI Won't Start When Engine Is Hot

I've got a 2002 Jetta TDI that's been playing stump the mechanic for the past two weeks. I've had about $800 worth of work (most of which had error codes and were necessary), but given that the next suggestion is to replace the fuel pump at a cost of ~$2k, I figured it was time to get some additional opinions.

When the car is completely cold, the engine typically turns over a few times before starting up. Sometimes a few turns into seven or eight, but I've never had it not start. The problem comes when I've driven it somewhere (like to the grocery store, yoga class, or to get gas, to name a few) and try to restart it after my task is done. The warmer the engine, the lower the chance it will start. In it's most extreme, the car will not start at all, and I have had it stall out on me at stoplights if I do manage to get it started.

The car has had a history of intermittent hard starts in the four years I've had it, but nothing at all like this.

In the past two weeks, my mechanic has replaced the coolant temperature sensor, thermostat and seal ring, serpentine belt tensioner and serpentine belt, power supply relay, fuel pressure regulator and seal rings and the crank sensor. They've also been able to see that something is off about the fuel pump since they can see air bubbles in the fuel line, but thought I could push the car for a while without having to replace the pump.