Do a volume test on the fuel pump. With the gas line disconnected, run it into a 1-quart oil bottle or other catch container. Start the engine and let it idle. It should run for 30 seconds or more on the fuel in the float chamber. You need to flow at least a pint of fuel in 30 seconds at idle. If not, check for a restriction in the flow from the gas tank to the pump before replacing the pump. It sounds like a fuel supply problem, not something internal in the carb. I have also seen a sticky float cause a fuel starvation problem, so be sure the float isn't hanging up on the carburetor housing and keeping the needle valve closed as the float bowl empties.
Jerry
