Ok, so I'm going to suspect a PCM issue here, but I want to be certain before you replace it.
I would highly recommend picking up a ELM327 USB capable device (if you have a laptop). Then we can use a Ford specific application to do more diagnostics and log pids.
Is picking up a adapter http://www.amazon.com/ScanTool-425801-OBDLink-USB-Diagnostic/dp/B005ZWM0R4/ref=sr_1_3?ie=UTF8&qid=1419352486&sr=8-3&keywords=elm327+usb an option?
Then we could do a remote session to diagnose further.
I'm not a "tuner", I am a ecu software engineer. Its different.
2011 GT500 = It gets me from A to B If you want good technical help. Put your Year, trim, engine, and PCM code in your post! Its easier that way