Okay, you're right. But the concept of the Minkowski space is nothing more than a vector space with a specific scalar product, that's why I was confused. Of course physical laws restrict motion in time. But they also restrict your spatial motion.
And if you're speaking of manifolds, I think that your Minkowski manifold is still four-dimensional (for each point there is a chart which maps it to the R^4, singularities excluded). And as far as I know you can map time to a specific component (of course you can, as in R^4 it is essentially a change of basis). Hence I would say that it is ok to speak of time as a separate dimension. Dimension is not a global but a local thing.
Speaking of moving through time, I think you cannot say that making choices slows down time. As time and the fifth or whatever "choice" dimension are distinct ones you can move through them independently. Just imagine a ball you throw: gravity pulls it down as entropy pulls you through time and the forward motion does in no way affect it (we neglect friction, relativity etc.). Movement through time is a uniform motion while the higher dimensions (the choice thing) doesn't even have to be topological manifolds. This means you cannot even define velocity, so a discussion about this doesn't make much sense.