"I encounter silvery areas or dark gray areas that won't come off no matter how much I rub."

You may have copper plating and it is simply worn away.
The first test would be to see if a magnet sticks.

If what you have is more than copper plating, you might try to clean it with clear ammonia full strength. This is harsh and corrosive. Wear rubber gloves, use it sparingly, and avoid breathing in the fumes.

Thanks for the responses. A magnet sticks which I believe tells me that it's not all copper. I need to reuse them with my doors so I'll proceed carefully. Thanks!

Maybe you could do a gold leaf on them. Craft stores sell gold leaf.