But more to your point, none of this is considered in earth orientation EO equations, one, because 100% of EO has already been attributed to local dynamics (torques on the oblate earth and a few thousand other things), and two because big frame motions are considered noise in the scheme of things. For example, if moving around a companion star in 24,000 to 26,000 years results in a current observable of ~50"p/y then moving around the GC in 240,000,000 years would only change EO by ~.005"p/y. So to come up with any major changes to the current inputs due to moving frame issues, would require that someone has been wrong about prior assumed inputs and values (which they are but really smart people do not like to admit when they are wrong - and most astrophysicists are really smart) or the whole theory needs rethinking (which it does but that will get you kicked out of school).
So yes, all astronomers now acknowledge the solar system moves, but no, none of it is in the EO equations, unless you get down to a micro-arc-second level, in which case it does not matter for purposes of this conversation.
Chinese Philosopher – Lao Tzu