You mean external disk, right? I don't have any other internal disk to install to.
Before posting this I rebooted yet another time, and the diskutil list and diskutil repairDisk outputs changed again. So I might as well leave it here. In any case I'll buy a 32GB flash drive tomorrow and follow that guide on booting from and come back to you.
-bash-3.2# diskutil list
/dev/disk0
#: TYPE NAME SIZE IDENTIFIER
0: GUID_partition_scheme *240.1 GB disk0
1: EFI 209.7 MB disk0s1
2: Apple_CoreStorage 185.4 GB disk0s2
3: Microsoft Basic Data 40.0 GB disk0s3
/dev/disk1
#: TYPE NAME SIZE IDENTIFIER
0: Apple_HFS Macintosh HD *185.0 GB disk1
/dev/disk2
#: TYPE NAME SIZE IDENTIFIER
0: Apple_partition_scheme *1.4 GB disk2
1: Apple_partition_map 30.7 KB disk2s1
2: Apple_Driver_ATAPI 2.0 KB disk2s2
3: Apple_HFS Mac OS X Base System 1.4 GB disk2s3
/dev/disk3
#: TYPE NAME SIZE IDENTIFIER
0: untitled *524.3 KB disk3
/dev/disk4
#: TYPE NAME SIZE IDENTIFIER
0: untitled *524.3 KB disk4
/dev/disk5
#: TYPE NAME SIZE IDENTIFIER
0: untitled *524.3 KB disk5
/dev/disk6
#: TYPE NAME SIZE IDENTIFIER
0: untitled *524.3 KB disk6
/dev/disk7
#: TYPE NAME SIZE IDENTIFIER
0: untitled *524.3 KB disk7
/dev/disk8
#: TYPE NAME SIZE IDENTIFIER
0: untitled *6.3 MB disk8
/dev/disk9
#: TYPE NAME SIZE IDENTIFIER
0: untitled *2.1 MB disk9
/dev/disk10
#: TYPE NAME SIZE IDENTIFIER
0: untitled *1.0 MB disk10
/dev/disk11
#: TYPE NAME SIZE IDENTIFIER
0: untitled *524.3 KB disk11
/dev/disk12
#: TYPE NAME SIZE IDENTIFIER
0: untitled *524.3 KB disk12
/dev/disk13
#: TYPE NAME SIZE IDENTIFIER
0: untitled *1.0 MB disk13
-bash-3.2# diskutil repairDisk /dev/disk0
Repairing the partition map might erase disk0s1, proceed? (y/N) y
Started partition map repair on disk0
Checking prerequisites
Checking the partition list
Checking for an EFI system partition
Checking the EFI system partition's size
Checking the EFI system partition's file system
Checking all HFS data partition loader spaces
Reviewing boot support loaders
Checking Core Storage Physical Volume partitions
Checking storage system
Problems were encountered during repair of the partition map
Error: -69716: Storage system verify or repair failed
Underlying error: 1: POSIX reports: Operation not permitted