It's not just about interaction causing collapse, or, if it is, a particle which has been interacted with and collapsed may be subsequently uninteracted with and uncollapse back into a wave.
http://en.wikipedia.org/wiki/Quantum_eraser http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser
Say you have a photon in a superposition of state A and state B - think position. If it is in state A it hits a detector, if it is in state B it does not. If the detector is hit, it displays 'HIT' on its screen - otherwise it does not. If 'HIT' is displayed, the researcher thinks photon was in state A, otherwise the researcher thinks it is in state B.
The result of the experiment, without any wavefunction collapse, is a superposition of two states of the entire system:
State 1: Photon is in A, Detector was Hit, Researcher thinks photon is in A
+
State 2: Photon is in state B, detector was not hit, researcher thinks photon is in B.
As you can see, the fact that the researcher never sees a photon in a superposition of states a+b (he doesn't ever see the detector both lit up and not) is explained without any wavefunction collapse.
Why are you assuming the particle has got to have a "position"?
The fact that a quantum particle can interfere with itself would be experimental evidence that it doesn't in fact have a definite position.
This part is not mysterious.
The mysterious part is, what in the world could be the thing that acts as a wave function and then collapse to a single point when it interacts with something else? What underlying reality does this hint at?