The spaghetti model seems all ok at first sight. But that is not all the story. Look at the old question why protons and positrons have the same electric charge. In the spaghetti model, charge is a topological quantity. Ok, let's assume that the topology argument is correct. But why then is the fine structure constant the same for electrons and protons?
Look at the model. It will not take you much to see that this question is not answered anywhere. In fact, the fine structure constant is not calculated, so far. Nobody can check whether the full charges of protons and positrons are equal.
Let me be even more specific. Schiller writes that the fine structure constant is the probability for seeing a Reidemeister I move. Ok, this may be so, but why is that probability the same for protons and for positrons? The tangles for the two particles differ and the number of strands/spaghetti differ! This is a problem. In my view, there is no good answer to the question. Why should the probabilities be equal?