OK, those who claim that a Crook's radiometer won't work in a vacuum,
please explain why. Every time I try to argue from first principles
and symmetry, I get that they will, in principle (of course, reversed
in direction from those in a low vacuum.)

Yes, in a vacuum it will turn due to radiation pressure, in the
opposite direction from the "regular" Crooke's radiometer. But the
forces involved are smaller so you need to cut down on things like
friction. For example:

A PSSC filmloop called "The Pressure of Light" shows some experiments
such as shooting a bb at a suspended metal bar to show that a
rebounding particle imparts more impulse than a particle that sticks
(they used grease to catch the bb). They also show a Crooke's
Radiaometer. It turned the "wrong" way. By refining the experiment
with an ultra high vacuum pump and hanging the vane from a quartz
fiber they were able to show the correct effect of light
pressure.
http://www.physics.brown.edu/Studies...emo/4d2010.htm