How to clean a copper pan from black burned fat chemically?
The crust is a giant mess of hydrocarbons that have been burned, caramelized, and congealed into the surface of the pan. 

I would recommend that you try the steel sponge to get some of the crust off, you may find that as you start breaking into the top layers of crust that it will fall apart. Another strategy would be to put the pan in the oven to the highest heat that is safe for the cookware and this might cause the pan to expand enough to create cracks in the crust or release it from the micro-cracks that were already in the pan surface. As a last resort you will have to chisel it off slowly.