Will it stay in a no-start condition long enough for you to determine if it's fuel or ignition related?
The park/neutral issue will be separate form the stalling. Probably a faulty neutral safety switch.
It is crucial to test for both spark and fuel at the time it is stalling. I suspect this may be why they can't find anything unless it has stalled on them.
In the event it is losing both fuel pressure and ignition spark, it could be the ASD relay getting hot and losing contact. The ASD relay operates both the fuel pump and the ignition coil. I have included some info about it below so you can be more familiar with it and how it works. If they cant get it to stall, it may be worth it to just replace the relay and see what happens.
I don't know where the vehicle is being looked at, but the dealer can hook up a device that will record and store live data and tell what the problem is. They connect it then have you drive it until it stalls then take it back to them for the readings that were stored. Its kinda the hard way, but is needed when it won't stall on them.
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