I have a V8 Dakota that I'm trying to straighten.

Elaborate on "fuel pressure problems". If it is dropping off after a few minutes, you might suspect a collapsing pickup screen inside the gas tank. Often that shows up as stalling when the highest volume of fuel is pumped, ... Which is during coasting.

Engine vacuum will make the fuel pressure go lower. The pressure will go up when manifold vacuum goes down, as in when accelerating. That is done by the fuel pressure regulator to maintain steady forces acting on the fuel; pressure on one side of the injector nozzle an vacuum on the other side.

What's important is what happens to that pressure when the problem occurs.

The goal of the fresh air intake system is to warm the air so the fuel will vaporize better. Liquid gas doesn't burn. It just goes out the tail pipe, wasted. That's why we needed chokes with carburetors. We dumped in a lot of gas in hopes a high enough percentage would vaporize to make the engine run smoothly.

The idea behind some air cooling filters is the colder air will be more dense so more can get packed in the cylinders, then you can add more fuel to go with it to get more power. The same thing can be done by pressing the gas pedal further. That may have some validity on other brands of cars that use mass air flow sensors in the air intake tubes. They use air temperature and flow to calculate volume so the results of an air cooling system will be noticed by the sensor. Chrysler is the only manufacturer that has been able to make an engine run right without a mass air flow sensor. They still measure the air temperature but engine vacuum is the main criteria driving fuel metering. The Engine Computer will still correctly calculate the fuel needs even when the air is more or less dense.

One thing that might confuse the computer is the discrepancy between the intake air temperature sensor's readings and the battery temperature sensor's readings. Those two will be the same when the engine has been off, and the computer expects them to be the same when the engine is running.

Don't know if that's the answer, but thanks for the information gregery. The world of auto manufacturing is extremely competitive. You can be sure if there was an inexpensive modification that would result in more horsepower or better fuel mileage than their competitors, the engineers would have incorporated it.

Monitor the fuel pressure.

If we assume it's not fuel-related, you 'll need a scanner to view live data to see what the Engine Computer is seeing. At cold start-up it calculates fuel metering based on air and coolant temperature and manifold vacuum. Once the oxygen sensor reach 600 degrees you will see the computer switch to "closed loop". That's when it fine tunes that fuel calculation based on whether it sees a too rich or too lean condition from the O2 sensors. If that's when the running problem starts, suspect something is limiting air flow and the computer is cutting back on fuel to correct the fuel / air mixture.

It's very rare for an intake air temperature sensor to fail but if it doesn't report the right air temperature, the computer won't command the correct amount of fuel. If the air is colder than what is being reported it will be too dense and the mixture will be too lean. That will result in a hesitation or stumble when accelerating, and a general loss of power. You would see that on the scanner as a temperature different than the actual temperature.

You also mentioned misfiring cylinders. Have you determined why they're misfiring? That can dump unburned fuel and air into the exhaust where only the unburned oxygen will be detected. In response the computer will try to add more fuel to go with that oxygen. That will flood those misfiring cylinders even more and will add fuel to those cylinders that are firing properly.