Update: I left it charging overnight (~13-14 hours). I just tried everything again, and there's been no change at all. No usb0 device, no /dev/sd* available.
I also tried fiddling with it on my windows partition, and windows is recognizing the device (like linux is), as a mass storage USB device. It even assigns a drive number to it, but the drive is not mounted or accessible any way I can see. It's definitely there in Devices and Printers, though, as Amazon Kindle.
I checked the device managed for USB/HID, but it doesn't show up in the list of Human Interface Devices.
I saw a thread about hooking up to the serial usb interface, but everything just went way over my head, and I can't seem to find any info on how to open up the kindle.