As far as the uncertainty principle: There's no guarantee that the uncertainty principle holds. Even if it does (and it probably does), I don't see how your time travel concern violates it anyway.
Alright, let us assume it does. Basically, what happens then is:
Suppose you measure the position of a particle two minutes ago. You then go back into the past, and again measure the prticle, but this time you measure its velocity. Hence, you know now both its position and velocity, shattering the principle into pieces.
However, I will admit this version has flaws. By going back in time, you will meet your past self, and the situation will dissolve into the "two physicists measuring both velocity and position of a particle" argument of Einstein against the uncertainty principle. I do not remember how, but I believe it was eventually overcome.
So let's try something else. You measure the velocity of the particle and then go back in time. You tell your earlier self, its velocity and instruct him to measure its position, which he then tells you. He then goes back in time to repeat the same, and you are now the sole possessor of the information of botha particle's position and velocity.
See it now?
If I measure the electron's position 10 minutes in the future, that won't tell me, with any certainty, where it was 10 minutes before I measured it (and therefore won't tell me its speed).
We're assuming here that everything that happened in the past stays that way in the future. If we don't, however, that would mean that your idea of an unchanging loop in time is flawed: it allows changes to happen.