So as long as the throttle is not moving, it runs OK? Light throttle, full throttle but not moving throttle? Is it the right carb for the engine, size wise?

I know you said the pump was new, but have you checked it lately? Does it dump fuel down the carb when you open the throttle?

If you carefully drive through the rpm range, does the engine run OK?

You need to determine if it's a true rpm related problem or it just happens to be you notice at the same rpm.

It would be pretty strange to have it act up at a certain rpm and still run ok on either side of it. Just for kicks, check the looseness of the distributor shaft, if the upper bushing is worn, it could cause some troubles.

You should also check the motor mounts, make sure the engine is not torquing over and pulling wires loose or pulling the choke closed. Stranger things have happened.

Joe