Well there is an advanced option for DoW mentioned in the rulebook, namely you let the two players roleplay the argument for a few sentences and then based on what was said determine the Duel of Wits maneuver that was used and roll the dice. I've never tried it myself so I can't say how well it works but it sounds like it might fit with your groups play style.
For me at least it helps if you think of the Duel of Wits as just another kind of Fight. No one ever talks about how their groups got ten minutes into describing how cool their sword fight was and then going to the dice felt awkward. Short statements of intent delivered with flair and then right to the dice.
When the GM grins, it is too late to run.