Vessbot
I am a bit hesitant to make a quick summary of the 737-800 speed stability.
But why not.
Firstly , it is not a very well balanced aircraft and not particularly stable. I have been told the -700 and the 300 to 600 as well is much better.
The -800 has a long fuselage that gives the elevator and the stabilizer a long arm.
Then power changes give rapid pitch changes that You have never ever seen, simply because no other aircraft has been certified with such large power/pitch couple.
The main problem is that anything but a small power change will cause it to overshoot its in-trim speed ( Or AOA if you prefer). And the natural stability is slow to stabilize if uncorrected.
The problem with the second Max accident is that he HAD to reduce power eventually, as the aircraft will go well past say M.95 in level flight at 10 000 feet, remember: 70 ton aircraft and 52 000lbs trust.
Anyway
The closest thing I have ever been to something similar is manual reversion in the sim, ie, no hydraulic for flight-control ,cables only and manual electric stab trim.
And there, it is all about small power input , get in trim and stay there. Descend and climb gently with power change, configure early etc.
With regards to the potential recovery of the latest Max accident one way would be to trim, reduce a bit of pwr, speedbrake. Get acceleration under control, dont sink, reduce power to get speed down towards 250. Then Flap 1 and speed 230, plus minus 20, get in trim, stow speedbrake re-trim.
With Flaps 1 you have a band from ca 190 to 250kts to play with and an elevator that can better overpower the stabilizer. As in above ca 270 to 280 kts : no chance ( with full nose down stab)
230kts is my go to speed in the 737-800 in any and all cases initially with control problems, THEN adjust or as per QRH.
DICLAIMER
Not blaming the accident crew.
Regards
Cpt B