So I've figured out a way to drill holes all over my living room floor and still do it tastefully.
Behold, the grommet:
I'm punching two holes in the floor, one near the edge of the wall by the fireplace, one near the other side of the room. I'll run the speaker wire under the floor, and pop it up through the grommets on the other side. I'm not sure if I'll have to glue the grommets into place or anything like that; we'll have to wait and see. Perhaps something heavier duty (metal instead of plastic) should be installed.
I went with 2" grommets with the assumption that someone may want to run cable, 4 speaker wires, and ethernet through the same hole at any point, so make the two big enough to accommodate that.
So here's to rational acts of destruction.