Garth - No prediction as I do not believe SS motion would affect the GR part of the experiment. It is my understanding that just as the GPB team has to remove the effect of the motion of the spacecraft around the earth (~5"), and remove the effect of the motion of the earth around the sun (~20"), so too would they need to remove any signal from the motion of the solar system curving through local space as all of these affect the abberation of light relative to the guidestar. For a graphic see:
Your calculation sounds about right for a brown dwarf scenario. And I agree it is doubtful that we would not have seen that type of object by now. Consequetly, if SS motion is confirmed in the ~ 50"p/y range, as the precession data leads me to believe, and we do not find anything in the 500-1000AU range, we need to condsider more exotic scenarios.
Mid April is probably optomistic. My guess is that due to the sheer volume of data (including possible unexpected signals) and the need to better understand and crunch that data, the GPB team will likely need more time. With an experiment this profound we should probably expect the unexpected.