Exactly what I was thinking Vilas. As you say, the SpeedSpeedSpeed got suppressed due to out of sequence actions. But we can't blame Sully and Skyles for that, the situation was hectic, there was no time for a flame-out checklist designed to be read from the relative calm of level 380.
Hence the thought of an insupressable sidestick shaker/vibrator/buzzzer that unambiguously tells the pilot he's in alpha prot.