Another fine point not usually mention after considering the order of magnitude arguements against a pure frame dragging explanation that would further rule out a stongly lensed or exploded version of frame dragging is that relativity would only concern itself with the total velocity in making higher order corrections. This would be the V_f values or total velocity at the time of periapsis. The simple but unusal empirical formula that seems to work to first approximation by Anderson et al is proportional only to the fraction of velocity that is hyperbolic, not the total velocity. Using the total velocity gives way wrong answers. But total velocity is what GR uses for its tiny corrections. Following a theory that would be based upon a magnified frame dragging effect would then give the wrong answers because of being based upon total velocity. It is a pretty "smart" anomaly to keep close track of what portion of the velocity is hyperbolic.

Regarding the formula, it is simple and elegant but not anything you would find in any standard physics text unless it was authored by Dr. Seuss. Usually when an equation can capture an anomaly to within an order of magnitude this represents progress. Sitll, because it may portend new physics, one needs to take care when comparing the theoretical result to the measured result. Sometimes the measured result is greater, sometimes lesser. Best fit for NEAR at less than 2%, worst fit for MESSENGER at 300%.

I've been looking at expressing the error as a tan (theta) so that the errors are either side of 45 degrees. This is purely arbitrary but since cosines of angles are used in the formula there can be no harm at looking at the error in geometric terms. But it is too early to look for any further physical significance to theta other than its expression as the amount of error. The first place to look to improve the fit and reduce the error would be to add corrections to the hyperbolic velocity component due to the moon and sun at earth periapsis. The text dealt primarily with Earth derived values in the first two equations which stands to be the major source, but the small additional values afforded by the sun and moon might improve the fit a decimal or more.