Accelerator pump wouldn't cause this problem. Its only job is to shoot a quick shot into the motor when you first crack the throttle, because when you do that at first you lose signal to the boosters because of the momentary loss of vacuum and lack of velocity, the engine will starve for fuel if it didn't have that shot to pick it up before it stumbles.
Under WOT or any steady throttle position the accelerator pump isn't operating or providing anything to the engine though. So in short, accelerator pumps are pretty much there to keep the engine from stumbling off an idle, or when going from off the throttle to on when moving.
You didn't say whether or not you have set/adjusted the floats, if you haven't, remember, its important to set the top out and the droop on them.
Another thing is to check and double check your timing, I see lots of people go after the carburetor when its a timing issue, you running a vac advance HEI unit?
You say it picks up after a couple seconds, during those couple seconds are the rpms rising normally with lack of power, or are the rpms being limited and then pick up after it cleans up? Also, does it act this way at a specific rpm? Like a happy spot in the powerband where it starts to run better, or is it just bogging until you're on the gas for a second at any rpm?