Quantum objects are particles, not waves. Particles are bundles of energy propagating on a field. It is the properties of the field that seem to give particles wave-like qualities. Thus in the Young's double slit experiment, a given particle goes through one and only one of the slits; it does...
The popular presentation of the HUP is incorrect. The HUP is about state preparation, not measurement. The bubble chamber is a good example of measuring on a continuous basis the position and momentum of a particle. What you can't do is prepare a state where particles in that state have both...