Thank you both!

Sounds like if I'm originating outside of the Schengen zone (which I am -- NYC), I'll be spit out landside after passport control. And although I could easily walk from one terminal to the other, I won't be able to get back through security without a valid boarding pass (which I won't have). Is that correct?

Thanks for the info about the public showers! The idea was to not have to shell out any money, but it's certainly better than nothing. Any idea if they're clean? I would hate to pay 15Euros and then be stuck showering in a hole.