..........just went through the same job on ALL chrome trim......as far as I know there is no rubber gasket, as I hoped there would be, so I used silicone behind the chrome before installing to prevent water to get behind it........you are on the right track with stainless steel screws.......I wished the "experts" that worked on the car before would have done so, would have saved me a LOT of work...come to think of, I used a small, barley visible beet of silicon around all exterior trim for the same reason.
CHEERS !
WITT !