Before replacing the cell, I would try to reduce the salt level some to see if you can get it to work properly. The last thing I would trust is a pool store test, they are rarely accurate. The best test I found is with a Taylor salt drop test kit and you might find that it matches your SWG better then the pool store test. At least it does for me.
Goldline cells will shut down when the current draw gets above 8 amps which can happen with high salt levels and certainly 4400 ppm would shut down the unit. This is done to protect the power supply from high current which can damage components. Also, these units will usually not read high salt unless there is really too much salt. I have also found that the SWG will sometimes read high salt if exposed to a hot water transient as from solar or a heater kicking on since the temperature increase makes the conductivity of the water increase which can then result in the current exceeding the 8 amp limit. Also, the cells will sometimes report low salt when the cell is nearing end of life even if there is enough salt.
For now, I would go by the unit readings over any pool store test since that is what really matters to the SWG. The SWG doesn't care what the actual salt level is only what it "thinks" it is. So I would try replacing some of the water before replacing any of the SWG parts. Besides, water is much cheaper.
Also, there is no separate salt sensor in the Goldline units. The cell itself is the salt sensor. They use the current delivered to the cell combined with the voltage and the temperature of the water to then calculate the salt level from the water conductivity. This is basically how electronic salt and TDS meters works.