During the melting, one can easily create a "reducing flame" to help reduce the oxygen in the
metal. That, along with Borax flux, is how I keep the Copper from oxidizing
while making ingots in the shop.
Your mention of Copper wires has sparked an idea.
How about a
solid Copper heatsink like a little porcupine? Should be fairly
easy to imbed some wire lengths into a molten ingot. Would require some
experimentation with the firecoat & heatsinking the wires I am sure. But if successful the
Copper spines should significantly increase the surface area to the air. And if all
works out should net a solid Copper piece instead of soldering on fins.