Interesting problem, make a good project for a student.

For your solution to work I believe it will need a fairly
thick copper base. Otherwise, as the heat is conducted
away from the burner by the copper, convection will cool
down the copper before the heat can be transferred to the
cast iron. This will be exacerbated by the small air gap
(insulation) between the copper and cast iron. Neither
will be perfectly flat.

A better solution may be to diffuse the heat by creating an
enclosed air box below the cast iron. Imagine the cast
iron forming the lid of a shallow oven which sits on the
burner. The air is heated by the burner and will result in
a fairly even distribution of heat. However, the downside
is that it will be both difficult to design properly,
clean, and heat up to the required temperature.

http://www.richardfisher.com