Randomness can't be predicted; that is the definition.
Also, you're assuming that reality is clear-cut and defined. This is wrong. The HUP is a fundmanetal property of realit, not a statement about observation.
The strings would also obey the uncertainty principle, however.
Yes, but then you get grandfather apradoxes and other such time-travel issues.
You're under the impression that the HUP is a statement about our capabilities to do measurement; it isn't. It is a statement abotu the fundamental nature of reality, and that statement is that
reality is fuzzy. It is not possible, even in principle, to short-circuit the HUP and get both a position and a momentum for a given particle. This is partially because the position of a "wave" is not really a sensible proposition.
(It's not possible to break causality form inside the black hole's event horizon. Spacetime doesn't let you.)