2004 V6 Acceleration Trouble, Help

My 2004 v6 mustang has been having trouble lately. 56k miles. Car begins to sputter/shake back and forth and hesitates randomly when im driving and looses acceleration. Sometimes letting go of the gas pedal for a bit will somewhat return it back to normal, but earlier today it got to the point where it completely stopped accelerating and i had to park and restart the car. Car didnt turn off tho, it stayed on just wouldnt accelerate at all. I have replaced the gas tank, gas tank filler gasket, fuel filter, spark plugs. Spark plug wires looked fine. Cleaned my throttle body and MAF sensor. I get no service engine light. Ive read online that it could be a bad coil pack causing the problem? Or a faulty fuel pump? 02 sensors? When i replaced my gas tank i put my old fuel pump in it. Not sure if its a fuel related issue. Any suggestions would be appreciated. Thank you

Havent been able to check the fuel pressure, and im sure i have no vacuum leaks. But i was also wondering if there is any differences between a v8 and a v6 fuel pump? Might just replace my pump with one from a GT and see if the problem continues from there. I believe this problem happens more often when i have my AC on.

Thanks for replying. I heard that if i use the gt fuel pump i will get less mpg? I was checking the coil pack for sparks and there was one that didnt really spark like the others. It barely sparked. Seems like its working tho cause when i unplugged it the engine started shaking. Might just replace the coil pack also.

Any ideas on what might be the problem. Anyone?

I just realized it only happens when i have the AC on. It losew acceleration, wont speed up when i step on the gas pedal. Will continue working as soon as i turn the AC off. What could be the problem here?