How would you call a gradual and continouos nose-down input that cannot be overrided by the sidestick? Half a fist full?
When above the AOA at which alpha Prot activates, the sidestick becomes an angle-of-attack demand input. Thus, at neutral the sidestick commands the AOA equal to the onset of alpha prot. At full back, it commands alpha max (just shy of stall AOA).
The scenario at hand has the AOA vanes freezing in a fixed position and the Mach number increasing such that that AOA now moves within the alpha prot range with the increase in Mach number . (recall that the stall angle of attack decreases with Mach numbers > 0.3).
So, as the Mach number is increased to the initial alpha Prot value there is no change, except the stripped alpha prot band is now visible on the airspeed scale - where you would not normally expect to see it.
As the Mach number increases, the fixed AOA is now closer to the critical AOA, and the sidestick must be pulled slightly farther back to maintain this same AOA which is now farther within the AOA range. (So, yes, perhaps "half a fist full")
If the airplane continues to accelerate, the problem continues until such point that the frozen AOA equals Alpha max at the higher Mach no. and now despite full back stick input the airplane attempts to reduce the AOA by pitch down. (which will of course, increase the speed /Mach and make speed/Mach reduction - even with idle power - shall we say "difficult."
Thus, the solution is to not accelerate (increase Mach) when this happens (or to decrease Mach to below 0.3), which in and of itself, would probably be enough. Of course to take the AOA out of the control picture is a more complete immediate solution, and one that would be required once you got to the point of having full back sidestick. Switching off two ADRs, leaves the computers with one source of AOA data (not enough to rely on) thus removing them from the flight control protection picture, and solving the erroneous AOA protection problem.