I have a slightly different different hypothesis. Quantum mechanics does appear to (based on my limited reading of the VN) play a role. One of Prof Tyr's disciplines is stated to be in particle physics. Specifically, I speculate; condensed matter physics.
The slight difference in interpretation of the story is that all matter in the universe at the subatomic level seem to adhere to the Heisenberg Uncertainty Principle (which you correctly stated). Hence it is not unreasonable to speculate that Prof Tyr's experiment might have something to do with manipulating the wavefunction of universe. Specifically the part about the "phasing" effect the MC experienced right being pulled into the reality of the story.
String and later M-theory propose a total of 11 dimensions (10 spatial, 1 temporal). It seems highly unlikely that the story takes place in any of those "spaces". Given that the laws of physics (at least as it is portrayed in the story thus far) largely resemble our own. Also, if the Airas system was originally the Sol system but in the far flung future. It still would not explain the lack of archaeological evidence that humans ever existed in our present morphology.
P.S. Physicist Roger Penrose and Anaesthesiologist Stuart Hameroff jointly posited a quantum origin for human consciousness in their Orchestrated constructive reduction (Orch) Theory. However, other researchers do not believe the human brain conducive enough for quantum processes to take place let alone affect reality.