I'd first want to prove the fuel pressure issue with a guage, then look at the voltage to the pump during the faulting sequence, if voltage is still good then chase a pump/tank issue, if voltage is dropping, causing fuel pressure to drop, then use the oscilloscope to check the fuel pump controller +ve and -ve in and out as well as the duty signal from the ecu. Once you know all these facts during the faulting sequence the answer will be in front of you. It is possible that the ecu is dropping its duty output to the controller, either deliberately due to one of the fuel metering calc sensors telling it to do so, or the controller output from the ecu is playing up. If the ecu is dropping the output deliberately, you will see the duty signal reduce gradually, if the output disappears all together the transistor contolling this output in the ecu is playing up.
Very easy to prove the basics on this one.
1. Connect mech fuel pressure guage at rail.
2. Connect multimeter at fuel pump.
3. Drive the car and produce fault, note the fuel pressure and voltage at the pump during fault.
4. Does fuel pressure drop? yes. Does voltage at pump drop? yes...test controller/ecu output circuits. no...look for fuel pressure loss at tank fuel pump module.
Do these tests, let me know the results and we will go from there. Sounds like your dealer doesnt have much talent in the workshop as this is really basic stuff for a good modern technician.
Cheers,
Phil.