I've documented the steps I used to fix it, minus a few wrong turns I took. :) Hope this helps someone:
- Download Kali Linux in order to boot it live for the repair
- Create bootable media from the ISO (I like YUMI)
- Boot the live Kali to the GUI
- Run the command df from Terminal and leave the results up for now
- Open Thunar, right click the HDD with the broken Kali install and choose mount
- Type the encryption password (this gave me an error which I just ignored)
- Right click the LVM and start the multidisk
- Wait a moment and then right click again and mount it. Unfortunately, this mounts it read only. No worries...
- Run df again in order to determine what was mounted and where. Compare the 2 df outputs.
- Now unmount it with: sudo umount /media/the-place-it-is-mounted
- Create a new directory for mounting: sudo mkdir /media/hdd
- Mount it as read/write: sudo mount -o rw /the/path /media/hdd (Replace /the/path with the partition you are trying to mount. You can determine this by comparing the results from the 2 times you ran df.)
- Use chroot to make the mounted filesystem be treated sorta like you booted into it directly: chroot /media/hdd
- Delete whatever you can to free up space
- Clean up the tmp files: rm -r /tmp/*
- Exit chroot: exit
- Close Terminal
- Go back to Thunar, unmount and stop the multidisk.
- Reboot into the repaired Kali install!
Remember, always keep good backups!!
EDIT: @blackMOREOps just reminded me of something...Don't forget to clean the Trash folder! I did this and forgot to document. Thanks @blackMOREOps!
Repaired OS: Kali Linux 1.0.6, 32 bit
Live OS: Kali Linux 1.1.0a, 32 bit