It would be a good idea to have two "tabs" in the log. One would be for combat and possibly inventory pickups, the other would be a dialogue log. You could switch between then by clicking the other tab. That would keep dialogue from cluttering up the combat window. That doesn't feel like it would be too difficult to do.

The idea to tweak the playing of dialogue so it doesn't constantly loop in real-time while in turn-based mode also seems like a good one. That seems like it would be a lot harder to do, but it should be possible, since the game has to keep track of how far from an NPC the camera focus is to decide whether to play a bark at all.