Perhaps my inability to sleep at home is my brain's way of educating me on the economics of the situation. You see, at home, I don't get paid to sleep. In fact, it eats into my free time.
Whereas, at work, I'm paid, and I'm here anyway so it's not like I can get any of my own stuff done. And they would frown upon me bringing in a games console and hooking it up at my desk. So I've got nothing to lose by sleeping at my desk and everything to gain.
I don't know why I didn't see this before. It seems so obvious now.