We found a spot for Bailey's skull rug: in front of the wall heater, right outside the bathroom. While he doesn't really fit on it, he still lies down and waits on it while someone is in the shower.
For our cross-country move, we didn't bring Bailey back to the house after it was emptied. This time, we brought him to the mostly empty apartment, but he didn't seem fazed. He did want to sniff and lick everything though.