2001 Buick Regal 3.8L V6 coughs on acceleration?

I replaced the spark plugs and wires, ignition coils, MAF sensor, accelerator position sensor, air filter, O2 sensor. None of that made any difference. It coughs standing still at 4000 rpm. It coughs upon acceleration from a stop, cold or warm. It coughs at 1500 rpm at 60 mph if there is an increase in grade. It stops coughing when I shift down from D to 3 (rpm goes up to 2000), so I don't think it has a cracked intake manifold or a vacuum leak. I checked the vacuum-driven diaphragms and tubes, but they are all sound. Gas mileage is always good (around 30 mpg). I haven't checked fuel pressure. I suspect that the power control module is giving false signals to foul up the ignition. Could I solve the problem with a new PCM? I tried to get a new PCM but it had a programming problem (security lock-out). Or is it a problem with the fuel injection system or fuel pump? Or something else?