Did you use 3/4 ply or something else? I have a bunch of 3/4 MDF but I'm wondering if the humidity would deteriorate it too much? Course I could line it with some showerboard or something... that way I could just wipe it out.
Slap on a good dozen layers of polyurethane on the box and it'll be good to go at 100% humidity. I have a pint coated over about 10sq feet of surface and it's as shiny as can be an holds water like a plastic cup. All pieces were painted twice before assembled, and painted about 6 times over after assembled. LOL Went over board at 15 when I had too much time on my hands.
We took a handmade solid wood dresser and coated it with a ton of coats of Helmsman Urethane and it's great in the bathroom with a sink dropped in it. I'd use that for sure on a bator. It's marine type polyeurethane, like on bar counters.