The problem is the instant you get airborne, you have the stick shaker AND IAS disagree. If you have the mental capacity to realise at this point that you aren't actually stalling (first instinct would be "oh sh!t, are my takeoff performance or flaps figures correct"), AoA probe failure wouldn't be my first thought.
Once you have had time and brainspace to process, "good, I'm actually still flying, no buffet, not stalling my speed & config are probably good", the next thought would be to notice IAS disagree, disconnect the autopilot (not engaged at this point) autothrottle blip blip off, lets climb at my initial performance tool target (if available ~15 +/- degrees). Now we are climbing away with a know thrust, known good pitch attitude, not stalling and that is going to get me toward a safe place (away from the hard stuff).
In all the confusion my buddy would probably be prompting me to turn off the flight directors too. At this point we have done the first part of the IAS disagree memory items, pitch and thrust to come.
This might make this sound somewhat logical, possibly easy, but believe me, that would be a REALLY bad day already and I might be between 400 to 1000' AGL before I can even begin to comprehend what MAY be wrong with my aircraft.
Boeing only gives guidance of 10 degrees nose up pitch and 80% thrust for this scenario. Would you really wanting do that with the stick shaker going off just after takeoff? It's going to climb like a dog and there are hills around and I have the SS going off, so I think I'm going to try to climb away for a while with some known good datums.
So, the problem is in this scenario disconnecting the autothrottle with the blip blip is actually going to leave you with takeoff, not climb thrust, not 80% N1 set. You may not revisit the thrust for some time because I still have the stick shaker. That is possibly a trap in all this. There is so much other stuff going on, that having takeoff thrust set is going to get you into the >230 knot realm real quick once you lower the nose to 10 degrees and forget to set the 80% N1 . Oh did I mention, that, at this point I may have to consider moving the stab trim switches to cutout too before retracting the flaps. Now I have to use the manual pitch trim wheel too as we accelerate.
I am actually now running TWO memory checklist simultaneously, the IAS disagree and Runaway Stabiliser. All because of a single sensor failure. Surely the certification basis for the aircraft is fundamentally flawed on this count alone.
Gums, the reason Boeing don't want to certify a new type is probably not so much the actual cost of the certification, rather the cost of type rating pilots. It was the operators who put the pressure on Boeing. Boeing knew if it was a new type they it would hand operators an opportunity to play the Airbus card against them, if you are going to have to put your pilots through a rating, does it matter if it is Boeing or Airbus?