I was pretty sure that Autodesk had to have created a way of keeping track of all those nifty dockables in Maya 2012, and it took a while to figure out where they put it. While the file where this data is stored is not exactly formatted for human eyeballs, I was able to read a bunch of things like "dockState," "dockControl," "dockWidget," and "toolBar", though, so I was pretty confident that I had the right thing. We closed Maya, renamed the file, opened Maya, and presto! The Tool Settings panel was working again!
If you run into this problem, the file in question is named "startupMainWindowState", and is the lone file stored in Maya's prefs/mainWindowStates folder. As I said above, it's not anything can can be edited manually (at least not easily). However, Autodesk did create a simple way to save and load the settings contained in this file. In the windowPref command, there are a couple flags that do the job: saveMainWindowState and restoreMainWindowState. If you make your own dockable windows or toolbars, those commands should let you save and restore their state so that you don't have to manually re-position them every time you make them. I haven't tested them yet, but I plan on doing so tomorrow, and will update this post with my findings.