- The configuration of the A320 for ditching with no engines running is CONFIG 3. I don't know how familiar are you with the flap configurations on A320, so I will start from the beginning. The flap lever has five positions: 0,1,2,3 and FULL (two configurations correspond to position 1-> CONFIG 1 and CONFIG 1+F).
In the CONFIG 3, which is the preferred method for ditching, the slats are extended to 22 degrees and flaps are down by 20 degrees. Config FULL, has slats down to 27 degrees and flaps down to 40 degrees. Look at the difference between flap deflection in CONFIG 3 and CONFIG FULL, that's 20-degree change in flaps. The 20-degree change will make a lot of impact on the drag of the aircraft and its vertical speed at the moment of impact. Therefore, CONFIG 3 is preferred. I must note that CONFIG FULL will not decrease the stall speed by a large amount: from my experience, it will decrease it by about 5 knots or a maximum of 10 knots. But definitely not more than that. The US airways flight 1549 had flaps down to CONFIG 2, below the ideal state.
If the ditching is performed with engine thrust, the suggested configuration for ditching is then, obviously, CONFIG FULL because we can trade engine power for the lowest possible approach speed which, for flight 1549, was not the case.
Flight 1549 was pretty close to the stall speed. On the video below you can see the approximate speed at the moment of impact. The exact touchdown speed was 125 knots.
With dual engine failure on Airbus A320, the aircraft will revert to alternate law, but due to the captain's fast reaction to turn on the APU, aircraft remained in normal law, assisting the pilot to not stall the aircraft. This does not mean that if the pilot pulls all the way back at such low altitude that no stall will occur. Upon landing/touchdown normal law goes gradually out and the FBW system introduces a nose-down pitching moment, so the pilot will not balloon the aircraft. In the last seconds before touchdown, the computer gradually returns to direct law, giving the pilot more feeling over the pitch. In this abnormal scenario, it is difficult to judge exactly what the FBW would do since this "reverting the pitch control to direct law" thing is characterized by the FLARE mode on the FMA, and I am not sure if the FBW system met requirements for that mode. If normal "reverting to direct law" occurred then the pilot would have been able to stall the aircraft just before the touchdown. If it did not occur, due to all abnormalities that occurred to the aircraft, the pilot would not be able to stall the aircraft.
The plane definitely does not know the correct pitch for ditching, neither what the crew was attempting to do. In ditching, the best pitch attitude for A320 is 11 degrees. In the answer that you linked, I can see that for 11-degree pitch attitude, the aircraft at the given weight is descending at -1 degrees, which makes the angle of attack equal to 12. Look the accident flight, angle of attack was 13 degrees, by the same analogy. That means that the aircraft was slower than ideal although the speed was 7 knots higher (due to the takeoff weight of the aircraft). The point is, given its weight the aircraft should have flown faster (than 125 knots) and the pilot should have pitched the nose of the aircraft higher, to match the preferred attitude of 11 degrees.
Stall pitch should be higher than the actual pitch for the ditching.