Basically, my plane keeps pulling either to the left or right, and at all times (when on NAV hold for the GPS) it is usually from 0.2 to as much as 2 nautical miles to the left or right of the flight path. It does hold close enough to the path that I don't get any vectors.
Sometimes the problem goes away temporarily, but after a while it may decide to crop back up and cause the plane to again deviate from the flightpath. Now, that in itself wouldn't be as odd, but additionally the plane is left pointing at the flight path, even though it's basically traveling parallel to it. What this means is that basically I'm pointing about one tick away from center on the HSI.
Here's some pictures to illustrate the problem:

and

(with stats)
Occasionally the plane returns to the flight path when a new waypoint is reached (on non-Direct flights)< but otherwise it stays a random distance away. When flying from Toronto to Munich (Direct-GPS), the plane actually went through some wild gyrations over the UK, where I thought there was some kind of turbulence.
Here's what I've tried so far, and hasn't worked...
Issuing the Center Ailerons and Rudder command - not sure if it has an effect because I have no confirmation
Checked and double-checked that rudder trim is centered, (I have no Aileron Trim on the A340, but this has happened on the 737 too.)
Saved and restarted the flight.
Engaging and disengaging autopilot
Ensured that de-ice and pitot heat are on.
Other than that I can't figure it out! Does anyone have any answers?
-Seth