The FCC does limit what can be emitted from a Class D amp, along with everything else. But not every unit is tested, only one unit unless it is a new model or a significant change was implemented.
Aluminum will do wonders for electrostatic noise if you ground it to earth. however, it is pretty transparent to electromagnetic noise. to stop that you have to use copper or preferably steel. However, whatever you use has to be grounded.
Are you having an EMI problem?