The stainless tray sounds like the perfect solution to the 'never leak' requirement, but I see two problems - it will have to be made up to fit the room in one piece probably welded together from two sheets ( 8' x 4' usual size ) it will be really heavy and awkward to handle you might not even...
If for some reason you don't want to cement on to the tiles ( antiques ?) then cover with thin plastic ( cling film ) and cement on top of that. Then if you need to reinstate sometime it all comes off clean.
How about that ?