I had the exact same thing happen years ago with STOCK GAS TANK, after having also upgraded it with a 3/8 pickup. Found out the pickup was uncovering under acceleration.

My guess is that there is likely nothing wrong with your fuel pump.

Cheap way to find out if its uncovering is to fill the tank completely full, right to the brim, and see if your symptoms change or at least lessen considerably. My hunch is that they in fact will, assuming the sock isnt plugged up from the car sitting around as long as it has.

My old car( running high tens at the time) i found if i let the tank get even close to only half full, it would do what yours is doing, generally in second, but sometimes in third it would start, roll out of the gas and get back into it, and it would be OK for a bit.Definately fuel slosh