There's no way to measure the transverse velocity except by tracking its azimuthal displacement, but that can't be measured very precisely. Maybe RadioAstronomer can give us an idea of how accurately we can place a probe at that distance on the celestial sphere, based only on its signal.
What about an uncalculated effect of cold gas mass on slowing the craft gravitaionally?(As for example, a rather depleted "solar wind"?)
The solar wind travels outwards at a pretty good clip until it reaches the heliopause, so for (at least) most of the probe's journey, it would be pushing the probe in the wrong direction to account for the anomaly. As for a cold molecular cloud, I think that's ruled out because any cloud dense enough to account for the anomaly would have an obvious absorption spectrum on the light of remote stars. Not only that, but I believe that a couple of the probes measure the local radiation directly; they'd see the cloud particles.
