Back to my question: the trim gains are a function of BOTH the autopilot mode AND the configuration, right?
Well, yes in a way. It is actually a function mainly of configuration. Both the autopilot stabilizer trim circuit and the main electric trim stabilizer circuit have two speeds, slow and fast. Fast is used with the flaps extended, slow with flaps retracted. The main electric trim (manual trim) is faster than the autopilot trim iirc. And of course, the fallback mode, manual trim, is as fast as you can turn that trim wheel.