The car suddenly dying - mine was doing that for a while, in the most inconvenient of locations. It ended up being the switch on the firewall, up behind the turbo, that's meant to shut the engine down in case of an accident. An Inertial Cut Off switch I think it's called. It's normally closed (short circuit) and when it goes open circuit it shuts everything down. Everything. Mine had degraded and was going open circuit with quite small bounces. I ended up disconnecting it, sticking a paper clip in the plug on the loom to keep it short circuit, and then taping over it with electrical tape. If that paperclip shorts anywhere else you'll blow a fuse elsewhere and get really odd messages on the dash. Don't ask me how I know, but swearing and few tears were involved before I worked it all out.

And another vote for the Waste Gate Modulator. If you accelerate too hard and the waste gate doesn't work properly, the ECU registers too high a pressure in the intake side, and to protect the engine cuts the fuel. Once the fuel is cut, pressure drops, and it turns the fuel back on. If pressure is still too high, it will cut fuel etc etc. It can start to surge.

A fuel pump dying will explain both of the above, but if you rule the fuel pump out, then these are two other options to look at.