It is correct that the uncertainty principle is not a statement about experimental precision as such.
It is incorrect, however, to state that you can know position and momentum of a quantum system exactly, because it presupposes such a thing as "exact position" or "exact momentum" exists. It doesn't, and especially not simultaneously. Any two observables which have a non-trivial uncertainty relation do not commute - and if they do not commute, not every eigenstate of one is an eigenstate of the other. So if you measure an "exact position", you get a position eigenstate, which is not a momentum eigenstate - it has no such thing as "exact momentum". If you measure its momentum, it becomes a momentum eigenstate, but now this state hasn't any such thing as an "exact position".1
The uncertainty principle is also not really about predictive power - quantum mechanics is fully deterministic in the sense that if you have any quantum state, its time evolution is fully determined by the Schrödinger equation. How this squares with the process of measurement is the famous measurement problem of how collapse, decoherence, or whatever else you think happens there happens. This is not the content of the uncertainty principle, the uncertainty principle is a statement about what the standard deviations are if you repeat the measurement on identically prepared states. In natural language, it tells you how much the individual measurements will fluctuate around the expected value, i.e. how much of an error you make when you think of the quantum state as having a single, well-defined value for the observable instead of a probability distribution. (This is your main error, I think - you keep talking of "position of the particle" and "momentum of the particle" when there really is no such thing for the quantum state)
For the somewhat unrelated question of continued measurement, if you continually measure a quantum state, you might evoke the quantum Zeno effect where essentially no time evolution happens because the system is forced to decohere before it had time to evolve into a superposition.
1There is a further subtlety that there are no such things as momentum or position eigenstates inside the Hilbert space - the "eigenstates" are not permissible physical states, and you can only ever measure position and momentum inside an (however small) interval dictated by your experimental configuration. Formally, the probability to measure any exact momentum or position is zero since points are zero-measure subsets of the real line, and the wavefunction is a probability density that has to be integrated to yield a probability.