Appreciate and understand everything you've said and it is standard crap chipboard, two layers of 18mm glued and screwed together.
My idea was to use a very sharp bolster or sharpened paint scrapper to cut betwwen the tile and adhesive. And then come up with some method of removing/smoothing the remaining adhesive, I was thinking a very coarse belt sander.
Why are you not keen on tiled worktops? is there any other covering that could be used?