Ralph,
If I were to try it, I would assemble the deep-dish and put it into the refrigerator for several hours, or even in the freezer for a while, to lower the temperature of the dish considerably before you bake it. Hopefully, the lower temperature will allow you to bake the pie without burning it. And I would put a sheet of aluminum foil over the top of the dish if the crust starts to brown too quickly. I don't know if these changes will work but, as chiguy says, it doesn't hurt to give it a shot.
Peter