During sudden accelerator pedal depress

You are on the right path. This sudden acceleration that causes a misfire or hesitation is from an imbalance in air/fuel. I would suggest measuring fuel pressure when this happens. Clearly there will be some drop in pressure when you accelerate but we need to see what the pressure is doing when this happens.

There are other causes that are covered in these guides. Let's get fuel pressure and then run through these and let me know what you find.

https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator

https://www.2carpros.com/articles/engine-hesitates

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

I have been burned many times by trusting what another mechanic did and assumed they didn't miss something. Let alone trust that the owner is relaying the info properly.

If the fuel pump has been replaced then lets assume that this is not the issue. However, that still does not mean that we don't have a fuel pressure issue. The only way to know is to check it.

At that point if the fuel side is okay then that leaves the air intake side. This includes the throttle bore, and sensors. Can you monitor the mass air flow sensor operation or MAP?

Have you checked for vacuum leaks?

There are a number of things that will cause this and we need to start eliminating them and the only way to do that is start testing them. Let me know what you find and we can go from there. Thanks

https://www.2carpros.com/articles/engine-hesitates

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

That is good news. Thanks for the update. I am sure that info will help others that visit the site. Glad you got it resolved. Thanks