95 trans am cuts out

i have a 95 trans am that i just bought. it has a 350 LI engine (or something like that)in it. the person that had it, put headers on it with no o2 sensors, so i installed o2 sensors. he also had a power chip, so i replaced that with the original chip. here is the problem. when you start the car, it runs rough and smells like its over fueling. when it goes to closed loop, the rpm's drop and it almost stalls,but it catches itself. once it warms up a bit, it seems to idle fine. when your driving down the road around 40 mph or so, and mash the throttle to the floor, is sputters and shakes, but if you just back off the throttle alittle bit, it goes just fine. i have also noticed that around 5,000 rpm it starts to cut out as well. i generally dont drive this fast, but if passing on a two lane road, sometimes it gets to that point. i am installing a new set of plugs, but not sure what else to try or to look at. i get no engine codes. also, what style of distributor system does this have? the plug wires go to the front of the engine down my the crank pulley.
thanks

Try new plug wire also....header can break down check wire quickly......
Have you checked the OBD for any codes???

I have a 95 camaro z28 it has the LT1 and it has been doing the same thing to me it only cuts out and stutters at 5000 RPMS in like 2nd gear when i put it to the floor. It wont do it as soon as i start it up and take off. Its only after i have been driving it for about twenty minutes r so. I have been told be several people that it could be the coil packs. Its not the plug wires because it would be cutting out all of the time.

The distributor is behind the water pump and is driven of the timing chain gear. Water pump and smog pump have to be removed to change cap and button. I had to make my own tool to take the distributor cap off and replace the rotor button.
Could be the coil packs.
Plug wires are a real pain to change. Make sure you have lots of time to change them.