Haoleb, the subfloor is a post-tensioned concrete slab, so cutting a groove in the floor probably isn't an option. I was thinking that flat wire might not present too much of an elevation problem under tile, but the runs are probably 25-30' (necessitating rather fat wire).
I am primarily concerned with any causitic or acidic properties in the thinset possibly damaging the wire insulation. Does in-wall wiring have better insulation?
It will be only a 4-5' run under the tile behind the couch, the rest under carpet and in/on the rear wall.