I’m curious why they would need that system in the first place. Pilots know to trim for level flight so the computer doing it automatically seems unneeded regardless of new engine placement.
There was, IIRC, a similar incident in an 737 Classic (go around in England that achieved a dramatic nose up pitch IIRC — not the Tailwind incident) but I can't seem to find the entry on avhearld.
https://www.gov.uk/aaib-reports/aar-3-2009-boeing-737-3q8-g-...