91' DX low idle? occurs at half tank and below.

[NoellyCanoli]

heard about the fuel sock problem from advance auto but the shop that replaced the tank, pump, sock, and filter was not supplied by that source. odds are high it's not the wrong sock but I am trying to gather info before I pull the tank and see. 

Symptoms of the problem are as follows. 

I'm Driving along at 45+ mph, full tank. Everything is fine. Once the fuel guage gets close to, and past the halfway point and I stop the car from 45+ to 0mph, the vehicle quickly idles down to dead nuts. I can start the car again with a bit of struggle and drive off again until the next stop light. I CAN keep the car running by feathering the accelerator pedal. 

Any Ideas? I don't want to simply adjust the idle a bit higher because I feel like that is hiding the deeper issue right?