How about a bad cold start injector? The idle is rougher when cold, then cleans up as the engine warms up, though it's still a touch rough then (as described in the beginning of this thread). If it's bad and leaky, it could still be making the fuel mixture too rich randomly as it shoots fuel into the manifold after the engine heated up. Does that scenario make any sense?
1989 560 SEL (black/black)
2001 Audi TT Roadster (silver/grey)