It's not willy-nilly nor staggering. The EAD (referenced in another post here) indeed talks about using the electric trim to fix the nose down problem, and then cutting off power to the system.
So add in the part where you can’t actually trust what your instruments are telling you, and the plane is flying like a demon has possessed it.
In the moment you are wondering, is the plane stalling? Is my airspeed actually what is being displayed? Why is trim not responding? My heart is beating 200bpm. Is that whooshing the blood in my ears or the wind?
The answers to these questions is obvious in hindsight. In that moment the flight had entered mortal peril. The question is not why didn’t the pilots recover from mortal peril with perfect hindsight. The question is how did this flight get into mortal peril in the first place?
My point is that it's easy to armchair quarterback the pilots whether they followed the checklist or went off checklist to do something better or worse. The problem started long before they got in the cockpit, though, and had been made evident once before at the cost of 189 lives. To continue to focus on pilots' actions at this point is missing the elephant for the flea.
The EA pilots already had gone off the checklist when they turned the stab trim back on.