... I have for some while been looking for a way
to test this, and finally came up with a simple statistical test on
local stars. For stars in perfect circular orbits, Doppler shifts,
together with the teleconnection correction, would cancel, but real
measured velocities show a wide random scatter. We can't measure the
true motion of any individual star without using Doppler, but if the
teleconnection is right then the radial component of velocity will be
overstated. I have been looking for a way to show that quoted radial
motions are systematically large compared to transverse ones. I

Have you included the systematic deviations from random
velocities due to the differential rotation of stars in the disk
and their actual, non-circular motions?

Suppose stellar orbits are elliptical, not circular. Then stars
in our local neighborhood will be a mixture of populations,
which we can describe as a) stars with semi-major axes
smaller than the Sun's, which are currently at the apoapsis
of their orbits, b) stars with semi-major axes about the same
as the Sun's and c) stars with semi-major axes larger
than the Sun's, which are currently at the periapsis
of their orbits. The orbital velocities of these populations
will be different in systematic ways. The number of stars
from each population which we measure locally depends
on the overall radial gradient of stellar density in the
Milky Way, and on some geometry.

It is possible that the effect of these different
populations could mimic the effect you see.