Okay, so I put a little extension on the outside so it wouldn't drain onto my truck paint and capped it off. Then I filled the drain full of CLR and left it for about four hours. I don't have any good news. It did clean it up some so it at least looks sanitary but the lower ledge of the drain just above the cross is very badly pitted and the chrome is no longer. I am going to look for a marine version that is made to deal with salt water. There should be one. The next time I go by a marine chandlery I'll investigate.
I'm certain the Elk Chilli was great, but I wouldn't blame your drain on it. That particular part wants to be stainless, brass or a more noble metal in that environment. The replacement is probably cheap enough to change out every six months if need be. The faucet is a bigger peeve for me.
When I find a solution for either/or will post, please do the same.