Continuing to use damaged cones in rear hub? I've read in many different places that if you take a hub apart and see damage on the cups, cones, or bearings (may god have mercy on you if your cups are damaged) That they must be replaced.

I recently bought a used bike that had a lot of miles on it. There was a tiny bit of damage on the cones in the rear hub, concentrated within about 1/8 of the race.

That seems to make sense: The wheel spun very freely, so it was well-tuned, and the top of the cones took very little wear. The damage developed where the rider's weight was: on the bottom 1/8 of the cone.

So I'm wondering if I can get away with simply rotating the axle so that the cones have the damaged side up, and the good side down. That way the damaged side will be supporting an insignificant amount of weight (and not messing the balls up), and my ball bearings will have the pressure on them while they're rolling over the good part of the cone.

Does that sound like a hack that will work?
No it would not work. The pitt didn't form just because it was on the bottom, the pitt formed either because the cone came loose, or an abrasive got into the bearings.

There's an equal amount of force being applied to the top of the cone as there is to the bottom when your hubs are properly adjusted. Think of the components in a hub as a stack, the cup is both the top and bottom of the stack, and the balls and cone are sandwiched in the middle, put some weight on the top of the stack and the force is going to be evenly distributed through everything. Your theory would only work if you left some play in the hub, which would only destroy the cones faster. 

Replace the cones and balls, they're cheap, and I imagine that you don't want to have a reputation of being a hack mechanic.