The fuel pressure regulator is mounted on the drivers side fuel rail that supplies the injectors with fuel. It looks like a small can with a vacuum hose attached to one side of it. Pull the vacuum hose off it and check for any fuel in the line. If you find any replace the pressure regulator. If the regulator goes bad, the engine can run with too much fuel being supplied or with too little fuel.

I would resolder the fuel pump relay just to eliminate one possible source of a stalling engine.

If the engine cranks okay after the engine stalls, then the alternator is not causing your problem. All it does is keep the battery charged.

When the engine stalls again and with the ignition off, disconnect the wiring connector on the mass airflow sensor(located in the plastic hose between the air filter housing and the intake manifold throttle body). Try and start the engine, if it starts right up the airflow sensor is probably bad and it's time for a new one. With the airflow sensor disconnected electrically from the fuel injection system the computer runs in a limp home mode with set fuel and ignition curves. The engine will not have the same power in this mode and may stall when you give it much gas, but it will run. If the airflow sensor is bad, check to see if the thermostatic flap in the air filter box is allowing cool air to flow into the intake manifold by pulling the silver hose off the lower part of the filter housing and checking to see if air is being sucked into the port(with the engine warm and running). If air is sucked in then the thermostatic valve in the filter housing needs to be replaced. If you do not replace a defective valve the hot air flowing over the airflow sensor will ruin it. For a temporary fix just leave the silver hose disconnected from the filter box.

Check out these few items and let me know what you find and we will take it from there. Good luck! John