To adjust the model for this effect one needs to scale the axis of the multivariate Gaussian noise differently.

But does the variation in the two different axis result from "how the dart travels", i.e. the physics ? To me it seems to be a matter of relative consistency of the angles with which one throws the dart. I remember reading an article that analyzed trajectories of basket ball free throws. They found for a given player their velocity of projection remained surprisingly consistent. Maybe that is true for throwing darts as well.