Sheppey
Next time you are in a simulator ask the instructor to give you a blocked static vent before take off roll starts. First hint there is a problem is after lift off when both the altimeter and VSI fail to register. A few seconds later the ASI needle stops increasing as the aircraft climbs and then goes backwards. That may trigger a false windshear warning. Eventually the reducing IAS sets off a false stick shaker.
Are you sure that the stick shaker in this case was false? It should only be triggered by AoA and is usually the one thing that can be relied upon with erroneous Air Data (certianly for Boeing and Airbus a/c). In the Birgenair incident already referred to the stick shaker was the only valid reference and they all the other warnings go off as you described. I too have done this in the sim and it w as challenging enough even when briefed.