Many carbs have a certain amount of 'adjustment' on the linkage that operates the diaphragm that squirts the fuel through the accelerator pump jet - essentially a nut is turned to load/compress a spring on the linkage.
If this nut is slackened, i.e. the load on the spring is reduced by lengthening it, the rate at which fuel is injected by the acc. pump jet is reduced. conversely if the nut is tightened, i.e. spring more compressed, the fuel is delivered faster and may run out before the engine has started to speed up, i.e. a sudden big dump of fuel, which can cause the engine to bog-down, followed by nothing more from the acc. pump jet (at least until the accelerator is released allowing the acc. pump housing to refill).
I'm not suggesting that this will cure the OP's problem, but this adjustment is worth keeping in mind if you want to 'fine-tune' how the pump jet works. Iirc, some official carb literature gives a time figure for setting up this linkage spring loading, i.e. how many seconds it should take for 1 stroke/operation of the acc. pump to pass through the pump jet.
Also iirc, some accelerator pump housings have a circuit (sometimes a drilling sealed by a ball and small weight) to allow fuel to be returned to the float chamber and not exit from the pump jet/nozzle when the accelerator is opened slowly - worth checking this return/bypass if the acc. pump isn't working correctly.
Al.