Shortcut Keys for Moving Desktops in Mission Control in Mountain Lion 10.8.x?

Are there shortcut keys for moving a Desktop in the array of Desktops in Mission Control?

I can now do this manually using the mouse by dragging and dropping, but I would like to do this with shortcut keys. Sometimes they even get re-arranged on their own (not sure how that even happens).

Regrettably I don't believe this is possible. As you've probably noticed, there are no user-accessible options for this in System Preferences' Keyboard Shortcuts. As far as I can determine, there aren't any scriptable interfaces either (plists, Applescript). Options for building your own program seem to be pretty limited as well, according to a mailing list post I found. The most you seem to be able to do programmatically is get the current number of open spaces.

The only way to possibly do this without some serious OS X hacking is to use something like Keyboard Maestro to do some GUI scripting to do the dragging for you. However GUI scripting is always a bit messy, and you'd need to account for the changing positions of the desktops, depending on how many are open, etc. I suspect that's not exactly what you were looking for, but it's probably the closest you'll get, unless someone finds something I didn't. Sorry.