I thought your cloak, and helmet, and shoulders stay hidden if you click on the stay hidden option...does it not? Correct me if I'm wrong. I'll try it out on the PTR when I get home.
Also, it's such a minor inconvenience. I love the new Transmog system as a whole because I don't have to stockpile a crap ton of armor in my bank or void storage. Stop complaining about minor inconveniences that are not game-breaking at all.