So, to complicate matters- I can't boot into safe mode. I let it sit for 48 hours and then powered it down. The status bar went about 1/3 of the way full, and then that's where it stayed.
So, I then booted into single-user mode and ran fsck -fy.
I tried to run Applejack, but it gave me warnings that it could not find the virtual memory space and that it was "only meant for OS X 10.4 and up" which makes me think that it hasn't been updated for 10.8 yet.
I booted into the recovery partition and ran disk repair and repaired partitions.
Later, I'll run Onyx to see if it does anything, but I'm not holding out hope at this time.
About the only other thing I can think to do is a new installation - but I really don't want to do that when I don't have a backup!