Hi,
that's where I would put it. Just make sure you have a little distance to the carbon plate (use thicker double sided adhesive or two layers) so the carbon does not take away too much of the radio power of the reader. Mounting too close to carbon or metal surfaces can reduce the useful range significantly. But I'm talking a few mm more or less, so it should work well there.
Kind regards
Eddi
Born to fly ...
forced to work.