I'm afraid I'm gonna have to drop the ball on discussion of extended objects. I can't shake the seeming-realization that restorative forces within the extended object must generate a gravitational backreaction, and down that path lies too much math to write down first (in order to summarize later), and I don't trust that starting with an English description avoids a gross mis-characterization.

However, I made a point about the expansion being in the curvature scalar, and Carroll has a lecture which supports this view for lambdavacuum (eqn 15 at https://ned.ipac.caltech.edu/level5/Carroll2/Carroll1_3.html ), which convinces me that I am not too addle-brained.

(The curvature scalar is the Ricci scalar, g^{\alpha\beta}R_{\alpha\beta}, written as R in the Carroll reference in the previous paragraph. Since the metric is Lorentzian a positive scalar curvature still leads to diverging parallel geodesics. Consequently we can say things about the positive energy theorem, and we don't have to introduce things like negative mass (and specify active, passive, or inertial mass when we do). By comparison, if we have a positive definite metric (+,+,+,+ signature) parallel geodesics converge in the presence of a positive scalar curvature. The sign difference for the timelike coordinate in our Lorentzian spacetime makes all the difference!)

Why does this matter? Because, at the Carroll reference, we can add terms for matter to the action integral, and following the logic in Carroll's subsequent paragraph, the scalar curvature is influenced by the matter. But note that by adding matter to eqn 15 we are making R even more positive. But in our universe with known matter, we can't make R go below zero. That's the conceptual keystone for me: quantum foobar doesn't lead to any energy state lower than that of vacuum any more than classical dynamics can, so there doesn't seem to be any room for expansion in local quantum systems or extended classical objects. (I guess the Newtonian-limit argument then goes that in vacuum if \nabla^{2}\Phi = 0 then you can't get an expansion force by adding matter.)

Finally, in part just because I love the image here, http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/n2ext.h... It's related to the first paragraph: if you spin an object this way it will shed gravitational waves (the metric isn't spherically symmetrical at any time) and at some level that must couple to the restorative forces that keep the wrench looking wrench-like rather than deforming during its spin. Turn the metal wrench into plasticine, for example, and it will deform while spinning, and the new shape will generate yet another different metric. If we put a fairly heavy weight on top of the metal wrench when it's on the ground, the metal wrench stays wrench-shaped; but the plasticine wrench would deform (and also heat!). Capturing all of this in general curved spacetime is not so easy, and for just weak Schwarzschild (as in the diagram, presuming the ground is our Earth) or even that and sliced de Sitter I don't trust the results to be general, so I kinda give up the moment. :/

My total guess though was that if the CC acts in the solar system than everything in the solar system, including metal and plasticine wrenches, need a tiny restoration force to avoid deforming. Could the notional equivalent of the spinning plasticine wrench in a comoving Cavendish appratus directly measure an expansion force within the plasticine? Likewise, does the CC affect the temperature of the deforming weighted grounded plasticine wrench? Not sure. I'm attracted by a comparison with a binary NS or BH system, treating BIGns----smallNS : Bigend--handle where the --- has been thinned out to almost nothing. We can extract local expansion from NSNS gravitational wave astronomy in principle. (A test system would probably galaxy-cluster scales in spatial extent or mass, though, see below.)

Undoubtedly these ideas will resurface in some future conversation.

Lastly, Cooperstock et al. https://arxiv.org/abs/astro-ph/9803097v1 grinds up some numbers; they take seriously cosmological correction to local EOMs at several sub-cosmological scales, and find out they're extremely extremely small, and compatible with not existing. Note that we've had 20 years of numerical relativity and physical cosmology not reflected in that paper.