But now the question is then, what dictates which path is seen for each observer in the spacetime?
The ideal type 3 time travel model should be able to produce the effect of "changing history due to stuff done by the observers", but BST, many worlds interpretation, deutsch model etc. does not provide a way to select between the many branches that depends on what happened at the branching points (where the observers will perform/not perform the history altering act), thus you simply cannot predict the evolution at the future light cone of the branching points (having said that I know almost…