Is this really true? I cannot mount an unapproved CD
player someplace
so that it won't flop around in flight?
yes

Actually, I spoke to our FSDO not too lona ago with this very question,
and the answer came back that it is legal to do so. The =installation=
needs to be approved (the installer can self-approve) but the device
being installed need not be an approved device, so long as it is not
powered directly by the aircraft system (cigarette lighter power is ok).

They are concerned that the installation not interfere with flight
controls and such. They are concerned that a non-approved device not
take the place of an approved instrument, but according to my FSDO, once
I explaned all we wanted to do (install an electric backup AI), they
were ok with it.

YMMV

Jose
--
"Never trust anything that can think for itself, if you can't see where
it keeps its brain." (chapter 10 of book 3 - Harry Potter).
for Email, make the obvious change in the address.