That depends on what brand tune you have and if the tuner encrypted it. I just recently had a car here at the dealer that the customer paid us to flashback to stock because nobody could get into it.
Nice write p. Be careful with generic keys. We see it all the time here at the dealership that when customers buy generic, for some reason they don't always retain the program.
You stated you knocked the cats out. Are you 15% that you got all of it out? If you have a piece wedged in there creating a blockage it can cause an issue
Contact Lethal Performance. They are a Ford Racing Dealer and might be able to get you a better price. Replace everything you can. Don't just do piece work. I can assure you that you will have to do the job again in the near future.
P0605 is Internal Control Module Read Only Memory (ROM) Error
P050E is Cold Start Engine Exhaust Temperature Out of Range
What mods do you have? Is it a flash tune or a hand held tuner?
I can check with a vendor that makes custom pipes. Include your name and address for shipping quote. Also the specifics of what you are looking for and I can get a price for you.