I have a 2

Which engine do you have; single or dual cam? If it's the single cam engine, remove the cam sprocket and check the dowel pin to see if it's sheared off. If it is, that will let the sprocket turn a little on the camshaft. That retards the cam timing, and that is picked up by the cam sensor on the driver's side of the engine. The late timing looks the same to the Engine Computer as a jumped timing belt. At the equivalent of one tooth off the Check Engine light will come on and the code will be "cam and crank sync". At two teeth off the computer will shut the engine down to protect the valves. At three teeth off the open valves will be hit by the pistons.

The first one of these I ran into behaved exactly the same way as what you're describing. If you monitor the output of the automatic shutdown (ASD) relay during cranking, you are likely to see it's not staying on steady. The voltage at the coil pack, alternator field, or any injector will be turning on and off randomly.

You have two conflicting symptoms. If you clean the plugs and it runs okay at first, you have to have sufficient spark to all four cylinders. In that case I'd be looking at an over-fueling problem. The map sensor has the biggest say in how much fuel goes into the engine. A vacuum leak anywhere will make it look to that sensor as though you're accelerating so it will call for more fuel.

Map sensors don't fail real often anymore, and when they do, they usually don't take real long, but in between the "good" state and totally failed, they can go through a short period where they report the wrong manifold vacuum value but it's within the acceptable range so no fault code is set. You'd find that by looking at the map reading on a scanner. You might try unplugging the map sensor. The Engine Computer will set a code and it will default to using other sensors to calculate fuel needs. If it runs a little better, look at that sensor.