I have a 2000 monte carlo ss 3.8 of course. Naturally aspirated. A couple months ago my car started to jerk or sputter whenever I accelerate. Sitting at a red light rpm jumps and drops as if it want to stall. So I started to Google and throw money at it. Here is a list a new parts I have e put on it.
SPARK PLUGS AND WIRES
ALL COIL PACKS
IGNITION CONTROL MODULE
UPPER INTAKE
FUEL INJECTORS
BANK 1 & 2 O2 SENSORS
IDLE AIR CONTROLSENSOR
MAF SENSORS
FUEL PUMP
NEW DOWN PIPE
and just changed THROTTLE POSITION SENSOR today and same results. I'm almost at the end of my road.

 

You most likely have a plugged catalytic converter
You have of course checked for Vacuum leaks right?
When you put the new fuel pump in did you replace the fuel filter as well should be done every 20000 miles looks like a short beer can in the fuel line under the passenger side of the car?

 

I experienced a similar issue with my brothers car. Wasn't all the same problems but close enough. We ended swapping out the computer ( PCM) and it solved the problem. Nothing showed it was bad , but like yourself we blew all the required parts at it and nothing worked. It was a few days without car for computer to get programmed Maybe others will have ideas for you. Good luck

 

IMO, I'd stop just throwing random parts at it hoping it gets better. You need to scan it and diagnose what is actually going wrong via the sensor readings and some simple related tests.

If you have no way to scan it and don't want to buy a scanner, take it to a professional who has the tools and at least pay them to diagnose it.