That was the first solution I had for #1. I'm currently at the following, but I think there has to be a better one because it's not clear that it would be possible.
G places the amulet in his safe, attaches his padlock and locks it with his key, then sends it to K, keeping his key. K receives G's safe, attaches his own padlock in addition to G's (there is a "large clasp", no mention of how large or how many padlocks it could support) and sends it back to G without sending his key. G removes his own padlock, and sends the chest back. K removes his padlock and has the amulet.
G places the amulet in his safe, attaches his padlock and locks it with his key, then sends it to K, keeping his key. K receives G's safe, attaches his own padlock in addition to G's (there is a "large clasp", no mention of how large or how many padlocks it could support) and sends it back to G without sending his key. G removes his own padlock, and sends the chest back. K removes his padlock and has the amulet.