From Lubos I learned about a new twist in the story of flyby anomaly. September twelfth 2007 Jean-Paul Mbelek proposed an explanation of the flyby anomaly as a relativistic transverse Doppler effect. The model predicts also the functional dependence of the magnitude of the effect on the kinematic parameters and the prediction is consistent with the empirical findings in the example considered. Therefore the story of flyby anomaly might be finished and dark matter at the orbit of Earth could bring in only an additional effect. It is probably too much to hope for this kind of effect to be large enough if present.
For background see the chapter TGD and Astrophysics.