We have original hardwood in the shower area, with no issues after 15 years. The occasional wetting gets wiped up right away, but with a few coats of varnish it is pretty impervious to that amount of water. I wouldn't trust laminate in that area, as the mdf under the plastic surface is just a soft sponge, and the joints expose it all to any spills. If you go with hardwood, you will be able to get the part that goes on the closeout cover planed down by 1/4" and it will all fit nicely. For the inspection port, you will need to cut the hardwood to fit, and if you leave it a loose fit, you can pull it up with a big suction cup (window suction cups are $5.00 at Harbour freight). If you go with new tile, you will need to add 1/4" subflooring everywhere, as there will be no way to reduce the thickness of the tile flooring.
I have seen a new vinyl flooring that is about the same thickness as laminate, and looks like hardwood. Installation is easy, it comes in "planks" and it is heavy enough that it just lays there. Use the suction cup for the inspection port.