VicMel, #4055, thanks very much for the detailed clarification.
Your views appear to strengthen the software argument, and in answering my questions clarifies the possibilities for local variation. But why just before takeoff (taxying bump, elect transient/switching) / just after take off; pitch rate again?
Stretching the hypothesis a bit more - higher takeoff pitch rate, hot / high operations, takeoff config / speeds, (takeoff pitch attitude limiting ?); also we might consider differences in training or in operating previous versions of the 737. Another pitfall of same type rating, minimum training requirement, no simulation?
Would a simulator (training or design) ever reproduce this type of software error ?
Opportunities for some alternative sleuthing.