With a 12 bore ball weighing 583gr. (.730" - pure) along with the copper tubing, probably .032" wall along with the steel screw, the weight would be over 600gr. - no slouch and an excellent idea.

I've a feeling I should try this in the rifled Mossberg pump. If a person could find some 5/8" ID pipe, it should run about 11/16" (687") OD. With a wad centered, tube filled and screwed tightly to the ball, the base wad would obturate to seal the powder gasses behind it and take the rifling as would a groove diameter ball (.724" in my 12 bore Mossberg), thus should shoot quite well. Length could be adjusted for best accuracy in whatever twist happens to be in the gun - ie: 35" or whatever you have. The copper tubing (or aluminum - some comes in standard ID measurements, while most copper is outside diameter) would not ride on the rifling at all, kind of a wasp waist bullet, reducing pressure and allowing higher velocities, if deemed necessary.
It is amazing what and how deeply a hardened 12 bore ball will actually penetrate if driven 1,500fps or faster.
According to Samuel Baker, through and through an elephant's head, ie: 'exit'. Sounds deep enough to me.

Thanks for this thread, Ed - MUCH food for thought with most of the thought already spelled out and tested.