Engine Sputters/Hesitates at 2000 RPM

My guess is you have Multiple fuel mixing problems.
Try and isolate it to a particular part of the foot pedal travel; ie ; less than 1/4 throttle, or 1/4 to 1/2 etc.
These are the things I would do, and in the order I would do them;
1) The first thing I would do is walk around to the back of the car and stick my finger in the tailpipe and take a soot swipe. I wanna know if it's rich or lean. Then I would start it up and listen to it idle. You can tell an awful lot about the low-speed circuits, the plugs, and the timing by how it idles.
3) Next I would verify the timing systems are all working properly, cuz that is so easy to do.
4) Then,I would verify the thermostat is maintaining it's minimum operating temp.and that you are not trying to run it too cold. My 367 likes 205*
5) And that the choke is fully off.
7) Then I would search for a vacuum leak. Including everything plumbed to the intake,the base gasket,the port runners, and the valley side.
8) Next I would blow out the low-speed air-bleeds.
10) If you have driven it and forgotten to shut off the choke, then I would replace the plugs.
11) I would make sure the secondaries are fully closing to whatever stop-system you are using.
12) If you have a mechanical cam, I would lash the valves, and add .002 to whatever your specs are.
Now we are ready to get into it;Next I would
15) check the float level
16) verify the gas is pure fresh gas
17) verify the T-port sync.
18) that the accelerator pump is properly adjusted, and not dribbling.
19) and that the PV is not leaking
20) And if I still hadn't found it, I'm doing a compression test.

You can stop as soon as you find the issue
But if you swiped the tailpipe and found it black, then I would go straight to #8 and replace the plugs.Then check the oil; make sure it is all pure oil; smell it and rub it between your finger and thumb. Then
Roadtest it, and if you have to; go back to #1,lol.
You know that's exactly what I was thinking....