I grew up in the woods — but woods 3000 miles from here, so this was not an animal I recognized. (Indeed, my intuitive thought when I caught my first glimpse of it was "Mountain Beaver" — an animal native to the Northwest, where I grew up, but certainly out of place here.)
More pictures here. Sorry for the quality: all I had was my iPhone, and I didn't want to go outside to try to get closer, as I was pretty sure I would only spook it. I was able to observe it for long enough to conclude that it was almost certainly not a predator. It was moving cautiously from place to place, foraging in clusters of plants, where it seemed to find things to munch on fairly frequently. It seemed to look around carefully before moving (I suspect there was as much listening as looking in that behaviour).
I think I know what it is now, because a FOAF came by while I was writing this post and identified it. But I'm leaving it a mystery in case someone gets a kick out of it that way. And to save myself from getting to bed any later.