When I have a vehicle that acts like yours the first thing I do I check the fuel pressure. The fuel pump may be good enough to start the engine and keep it running and driving under normal, non-aggressive driving but it may not be able to supply enough fuel volume that is required under heavy acceleration and wide open throttle.
If you had a scan tool you could look at the fuel adaptive memory and see if the PCM is trying to add excessive fuel under heavy acceleration. If that is the case then you would know that the PCM is doing its job. Grab a fuel pressure gauge from Harbor Freight or rent one from the local parts store and see what you have.