First, I think it should be clarified that when out of trim it is almost impossible to bring back using the manual wheel. It is possible with the electric trim switches. [...] It seems to me that the design of the wheel from the beginning was to be the backup in the event the actuators failed and that the normal use would start with an in-trim or close to in-trim state.
About your first part, I share the concern about understanding why all the existing FDR data on the MCAS induced out-of-trim, from JT043, JT610, and ET302, shows consistently that all the pilots stopped too early the manual electric trim correction just before using the STAB TRIM CUTOUT. I think that the badly redacted procedure play a big role here. In that procedure, the worst and imminently fatal situation is documented at his end in a small notice. The procedure should have been designed to survive the worst and urgent case first in bold. The training must also be more specific on that point. Finally I also suspect that the pilots, for some reasons, did not feel correctly when the stab trim neutralize the elevator pitch. I speculate that this could be when both pilots activate the yoke pitch: the pilot using the electric stab trim stop when he feel the pitch force neutralized on his yoke, without taking account of the pitch force on the other yoke. Regardless of the reason, this neutralization issue should deserve a better analysis in my opinion.
My non-professional opinion - as a lowly PPL - is that pilots are simply not used to use electric trim continuously for several seconds on end (e.g. more than 5 seconds). In normal operations there's simply no reason for the stab to be so severely out of trim that several seconds of continuous AND or ANU inputs are required to stabilize the aircraft. Long trim inputs are actively disouraged and reprimanded by instructors during initial training, and a lifetime of practice cements the muscle memory imperative "trim inputs shall be short and to the point; repeat if needed".
Of course, this does not explain why the ET302 pilot repeatedly seem to stop trimming at exactly the same stab position (i.e. way too early); maybe he simply kept trimming for the maximum number of seconds he felt were safe, wich was the same number in both occurrences. I am aware of your hypothesis about both pilots pulling on connected yokes, but this also does not explain why the trim movement stopped repeatedly at the same stab position (unless one of the pilots kept imperturbably pulling with constant force throughout the whole mishap duration).
I agree, this is something still to be explained satisfactorily.
Note: All of this should have been different if the 737 MAX still allowed to cutout the FCC stab trim without cutting the manual electrical trim, as in early 737 models.
The dual stab trim cutout switch design originated in early 737 models, but the possibility for pilots to disable FCC stab trim inputs without completely cutting out the electric stab trim motor is still there in all NGs flying as of today. This possibility was only removed with the MAX, and then willfully mis-documented as a mere "labelling change" of cutout switches. In my opinion, the explanation that this (apparently absurd) design decision "just happened" coincidentally with MCAS introduction (and it's obfuscation in FCOM, and mis-representation in certification documents) just doesn't fly.