Really cool project! It might be interesting to note that the mentioned time travel paradoxes can be solved by using probablistic states (as multi-valued interpretations of quantum mechanics would imply would be the case in any real system with time travel). And that this results in a computational system that can solve 'uncomputable' problems like the halting problem. See https://arxiv.org/abs/1609.05507. Time travel is really fun to think about in a computational setting!