gravitational waves - Does rotation always slow down in general relativity?

Suppose I have a rotating object in empty space. Will it lose angular momentum due to interactions with spacetime?

The most obvious case if if the object has a quadrupole moment. Then the quadrupole formula simply tells us that it will lose energy and the angular momentum ends up in the form of gravitational waves. Normally the dipole moment is ignored as a source of gravitational waves since it is to lowest order the total momentum of the system, which is constant. At least in the linearized case conservation laws make a quadrapole-free object non-radiating.

A rotating axially symmetric object (whether matter or a Kerr black hole) would hence remain rotating forever in GR. However, at least the Kerr space-time is infinitely old: the black hole has always been there and always will be. A realistic spacetime where a mass implodes to form the black hole will be time-asymmetric, and the rearrangement of matter could presumably move some angular momentum to gravitational wave modes. Hence objects changing over time may lose some angular momentum. But generally axisymmetric objects have a hard time emitting gravitational waves unless they have higher-order moments (or internal flows producing gravitomagnetic quadrupole moments).

Overall, these considerations seem to fairly strongly push towards the conclusion that ideal objects never slow down their rotation as long as they have zero quadrupole moments. But non-ideal objects presumably have at least a tiny quadrupole moment by virtue of being composed by atoms. A sphere made up of $N$ random point masses has a quadrupole moment tensor where each component is the sum of $N$ finite-variance random numbers; the central limit theorem indicates that the components will be Gaussian and we can hence assume a $1/\sqrt{N}$ residual quadrupole moment. Using the estimate in this paper for a neutron star with a bump that suggests a spindown timescale of $$\tau \sim \frac{5}{4\pi}\frac{1}{f}\frac{Rc^2}{Gm}\left(\frac{c}{v}\right)^3\sqrt{N},$$ where $f$ is the rotation frequency. Since $N\sim 10^{50}$ for Earth and $10^{57}$ for stellar-mass objects we should hence expect a very slow but finite spin-down time.

Does this make sense?