[J.C.]

Fuel pump?
Cam syncronizer assembly or the electronic sensor?

Ask them if they had a look at any of the above in their 3hr diagnostic "playaround". The cam sync assembly is an easy one to see. Removal of coil packs and the sensor unit is required, then grab the shaft and see if you have excessive movement which opens up the gap between chopper pin and sensor. If gap is to great, sensor cannot read and engine feels like it is running out of fuel as it reads, then doesn't shutting it down, then reads again and fires up again. This process happens until the engine losses power and mobility and shuts down completely (stalls).
Hope this helps somewhat.
Regardless of the dealership issue, let us know what you find. It may help someone out.
Cheers.

PS. If it is the cam sync mechanical unit that has to be replaced, ensure you replace the sensor also. Been there, done that.