I was re-watching the first season of 24 with my girlfriend, and I kept thinking that, scene by scene, these conflicts could work well in Dogs.  The NPC knows something: how far are the PCs willing to go to find that thing out?

But I think that it would have to be set in a city to get the right feel of a conspiracy.  And so I had the idea of having the PCs deputized by the TA and sent back east.  There, amidst what pass for the Faithful back east, they have to unravel this conspiracy.

I haven't really gotten much farther than that, I'm still thinking about how to stress the time factor, and about what on earth would possess the TA to go and deputize three Dogs.

Mechanics:

A conflict begins.  We're talking.  We each roll Acuity + Heart.
It escalates.  We roll Body + Will,
Now guns are drawn.  Do we roll Acuity+Will, or (since we've already rolled Acuity and we've already rolled Will) do we just get whatever dice our Guns possess?

Yeah, pretty much:
Start Talking: Acutity + Heart
Escalate to Fighting: Body + Will
Escalate to Shooting: No stats are rolled (you've already rolled Acuity & Will in this conflict).

You get to roll your gun dice when they first get brought in via a Raise or See, even if you are just talking. You don't have to pull the trigger or anything.