If you happen to get into a bad situation declare the emergency. Solve the life-threatening problem, and then work out the legal one. The sanctions are far less permanent. The radar plot indicated a normal slowing upon intercepting the localizer. It appears that the aircraft stalled around 80 kt, which is at least 20 kt higher than normal.
Ice can dramatically increase the stalling speed.
That means the pilot must fly as fast and as straight as possible. Go for an airport with a long runway because the stopping distance will be much longer than usual. MEM was a good place to go. The other absolute is not to use flaps when carrying airframe ice. This could result in a tail stall and cause the aircraft to nose over abruptly.