I definitely started out with a hyperactive "left-brain," but then it blew a fuse (or something) and now it's actually hard to be very analytical.
In a way, it was actually a little helpful, in that I seem to make fewer anxiety-due-to-over-analysis type screw-ups. But all the other kinds of screw-ups still happen. And there are some new ones due to slower cognitive processing (hard to keep up with what people are saying).
So, I guess that goes to the point that "over-thinking" is not the fundamental problem, and so stopping it is not a fix. In fact, as I recall my attempts at trying to be 'spontaneous' were met with some shock and horror. Apparently, it's possible to do that really wrong.