'Ere ('ow queer...)!
Just been hard at work on sommat for my employer, and in that marvelous way that sometimes happens when you're thinking about something else, I think I've worked out why you all have been having such a hard time with the DC-3 AP.
Do y'all get your pitch trim right *prior* to engaging the AP?
Since I really enjoy flying props (single and multi-engine) when not flying the 738, and I have my control setup optimised for them (props, that is. I've got two control config files so I can switch between props and the 738 in a few seconds), I have rocker switches devoted to pitch and rudder trim, and invariably I tweek the trim during climb out without really thinking about it.
When time comes to engage the AP it doesn't have to do very much to remain in the climb I've been hand flying up to that point - remember, FS AP uses pitch trim to maintain V/S. Sure, the nose dips as the AP catches up, but not by very much, a dozen feet usually.