The only thing I can think of that might work is a floating tile flooring that is put down like the laminate flooring you have probably read about in this forum. In short, instead of having a "wooden" finish,it has a thin layer of a ceramic material. It also comes in more of a square or tile shape (about 12"x12" I think) instead of the strips. It's made by the same companies that make the wooden laminate, and locks together in a similar way.
While I'm no tile expert, it is something I'm trying to learn about. To that end, I often go to this other forum concentrating on anything "tile". One of the more spirited discussions there concerned using tile in floating installations, specifically that made by EDGE PRECISION.
You might want to ask there about using cork as an underlayment. They have many professional tile installers and contractors.
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