My tricky fix wasn't as simple as it seemed.
 

So, I just got my car back from the mechanic. I thought they had the problem, but it turns out not so much. Here are the confusing circumstances:

My car started misfiring (po300 random cylinder misfire). This rapidly progressed until the car could barely start and then stalled immediately when the accelerator is pressed.

I replaced the spark plugs, ignition coils, and wires. The problem was no better.

They replaced the fuel pump, the fuel pump relay, the fuel sock, cleaned the throttle body, cleaned the mass air flow sensor, seafoamed the entire intake system, cleaned the EGR valve and tried a replacement EGR valve. None of this fixed the problem whatsoever.

the only thing that does help - and it helps considerably - is to disconnect the EGR valve's electrical connection/computer connection. With the valve disconnected, the car still runs slightly rough, but much much better than with it connected.

What does this mean? Where do I go from here?

Here's a list, go nuts:
My car misfire was poor exhaust flow.

Missfires Can Be Caused By a Million and One Things,

Vac Leaks
Wiring Issues
Spark Plugs(Even Fresh Spark Plugs That Are Crappy Quality.... E3 And Such)
Ignition Coils
Alternators (Search EMI)
MAFS
Injectors
Injector O-Rings
Intake Gaskets
TB Gaskets
PCV Hoses
PCV’s
Malfunctioning EGR
Malfunctioning CAS
O2 Sensors
Aftermarket Intakes
Intake Hoses
Vac Lines
Timing Chains
Timing Chain Tensioner
Broken Cam Gears
Malfunctioning Cam Sensors
Incorrect Crank Gears(The I4 Has Like 40 Different Configurations For Whatever Reason)
Incorrect PCM Flash
Issues Within The PCM
PCM Wiring
Bad Diaphram Within The FPR
Issues Within The Fuel Pump
Dirty Fuel Filter
Dirty Fuel Lines
Pre-Cats/Poor Exhaust Flow

If the above gaskets/seals have not been changed, change them. Clean your MAF sensor, throttle body.
Change your PCV valve and probably that short hose as well.
Inspect the intake accordian tube for cracks. Inspect for vaccuum leaks.
Put in a good Fuel system cleaner: Red Line Synthetic Oil - Gasoline Fuel Additives - SI-1 Complete Fuel System Cleaner
Inspect wires. Re-set ECU after doing above.

What do you think it means, though, that the car runs better (not perfectly) with the EGR valve disconnected from the PCM?