Ran the update. Same problem.
Deleted all those files. Same problem.
Seems likely that it's in the user library if it works for another account, so you might want to rename the Adobe InDesign folders in ~/library/preferences and ~/library/caches.
And did you check the crash report afte the update to be sure it is the same?
I FIXED IT!!
For people who have this problem in future:
When trying to edit a file in Coda 2 it gave me a warning it couldn't edit a file in ~/Library/Caches/Coda 2 as it didn't have the right permissions.
I took a look and sure enough it was set to 'Read Only'. So I edited the permissions of ~/Library/Caches to to 'Read & Write' and BOOM, InDesign now launches.
Thanks to Panic for helping me diagnose Adobe's problems due to Apple's lousy Time Machine restore!
Note: Adobe, write clearer crash reports!