The exterminator came yesterday, but couldn't find any evidence of an infestation. No holes, no droppings, nothing at all to suggest that rats have taken residence or even ever lived here. Of course, the house was devoid of the scratching and squeaks while he worked, but after he left, sometime late in the evening, it started up again.
I talked to Chelsea about it earlier, and she said she didn't notice any noises during the day. It seems it only happened late at night, after she falls asleep. It didn't really surprise me that the sounds woke me, but not her, since I'm a fairly light sleeper, and she's slept through tornado sirens before. So I woke her. And she said she didn't hear anything. She may be a deep sleeper, but she's not deaf... I don't really know what's going on, but I'll think of something later.
I discovered that, while extremely uncomfortable, wearing earplugs helps with sleeping. So for the first night in a while, I've gotten some relatively good sleep. I'm still a little off, but I'll do some thinking and try to get that post in for the docs later tonight.