and the suspicion is that it was physically too difficult to do it manually at that point.

In older flight manuals for the earlier models of 737, there was a specific paragraph that spoke about the aerodynamic loading of the tailplane preventing manual trimming in high speed flight. And then there was a description of a technique to let the aircraft pitch down (unloading the tailplane), rapidly wind on some nose up trim, then pitch it up again - repeating these yo-yos as necessary.

The newer 737s have exactly the same design of the tailplane and manual trimming system (this would not meet modern design rules but was grandfathered in), but the Boeing lawyers had that admission of a design limitation (and the work around) removed from newer flight manuals.