The coax is a fine lead-in cable. At the receiver, connect the shield to the same terminal as the external ground, and in the attic, make sure the shield is cut away carefully.

Keep in mind that the antenna doesn't "begin" until it emerges from the shield. Solder the joint, heat-shrink it, and make the largest loop around the attic you can, closing the loop.

I've never heard of using 5-gallon cans as antenna cores, so I can't comment intelligently about the idea. I can, however, think of several unintelligent comments, but I'll refrain.