What kind of bathroom tile is this, and what kind of drill bit does it require?
I still don't know entirely what type of stone this is, but a 1/4&quot; carbide-tipped hammer drill bit went through it with no problem, and no cracking. I didn't end up using a hammer drill, just an impact driver. The main challenge is that the bit wanders at the beginning, but I think that is a general challenge of drilling in tile.