Copper has about 400 times the conductivity of firebrick. The moment you open the door of the BBQ, any heat stored in the copper will vanish and the bottom of the pie will scorch while the top stays pale.
Since you have firebrick available to you, I would make a ceiling out that. I'm pretty sure Home Depot carries angle iron. Either buy it there or track down an old bed frame. Use the angle iron to suspend rows of firebrick above the hearth, using the bricks you have now for supports.
Speaking of the supports, while some heat does collect in the headspace of a bbq, it's mostly a bottom to top heating scenario. Firebrick is a powerful insulator, ie, it lets very little heat through it. The supports, where they are now (flush to the brick), will prevent heat from getting to the ceiling. If heat can't reach the ceiling, again, your stuck with a bottom that finishes long before the top.
So, build a ceiling, if possible, that extends past the sides of the hearth, and push the supports out- way out. The hearth will stock block a considerable amount of heat, but you'll get more rising heat to the ceiling without the walls in the way. You can also help even out the heat between hearth and ceiling by cranking the heat up for an hour (or more) and the turning it off for a while (maybe half an hour), allowing the heat from the hearth to rise to the ceiling a bit, and letting the ceiling heat (with very hot edges ) even out.