I got an error saying that KCT couldn't load the its configuration file and that I should post my log here.
Here's the log (at 3.7GB, none of my text editors will open it):
~wrong log, had to remove from dropbox to upload other logs~
I'm assuming that my install is irreparable, but I'll keep it around for a bit in case someone wants more info from it.
I'm further assuming that the cause of KCT/KSP breaking is that I successfully modded KSP until it broke, so I'm just posting this in case it proves useful to the mod makers.