I just wish those dialogs wouldn't pop up while the game is paused. What the heck, are they on a random timer? If the game is paused, I don't want to be interrupted!
Whichever timer the meetings are on is separate from the one the dwarves are on. Each action you take with the interface (designating, constructing, etc.) advances the meeting slightly, even while paused.
Try this: Once the conversation starts, pause, and then scribble designations with the mouse*, and the conversation screens should start coming right up. You can use this glitch to make the entire negotiation happen in an instant of dwarf-time, thus preventing your leader from going off to get a drink or something and delaying the meeting for a year.
*It also works designating things with the keyboard, but the mouse is faster because it makes each square count as a separate action.
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As for improving things: I think the best way to make the dialogs less intrusive is to do something like this: Make a screen for diplomatic options (maybe off the Civilizations screen) that the player can access at any time, and use to set things like "what stuff we want to negotiate for", and "what kinds of terms we are willing to accept from them", etc.
Then when the meeting takes place, your dwarf negotiates based on those settings, rather than asking you every time. The dialogs could be completely eliminated.