Steve,
The spacetime metric adopted by the IAU does not have enough terms in
it to generalize to a solar-system wide coordinate system with full
precision of current atomic clocks in the vicinity of rotating,
gravitating bodies. In a rough sense the metric was designed to
permit the definition of a self-consistent coordinate frame out to
around twice the geostationary radius.
In the broader sense, even a solar-system barycentric coordinate frame
is suspect at the level measurable by current atomic clocks, and that
is part of the motivation for the various international scientific
unions recommending the establishement of a pulsar-based time scale.
I am not an astonomer and am not familar with all the associated
literature, nor am I a relativist, nor have I done precision studies
(yet) as they pertain to such.
With that said, and being too lazy / busy to immediately delve into it
myself, do you know of a citable reference that supports what you just in
so many words?
J.Seago