My guess is that either a failing fuel solenoid or fuel solenoid driver blew the fuse. Now either the fuel solenoid is stuck, giving full fuel, or the FSD is shorted, doing the same. When the PCM sees the engine is running away it drops the fuel cutoff solenoid which causes the stall.

Check the fuel solenoid first by applying battery power directly to it after removing the wire from the FSD. If it clicks, the problem may be the FSD. I would not try a new FSD until you comfirm the solenoid is not shorted as it may kill the new FSD too.