Thanks for expounding the implications of your model as it pertains to time travel.
As a clarification, I am in no position to say whether Alex is right or wrong about time travel. I think the vast majority of physicists see time travel as impossible. Not because it is forbidden by the equations of relativity, but because rather because of the paradoxes of causality that are well known.
In any case, the issue for me is whether there are inherent problems with time travel as it pertains to the equations of general and special relativity. If there exists such inherent problems, then I'm surprised that people like Hawking, Thorne, Gödel, et al. did not recognize those problems and that we are now having this conversation.
I believe that Alex may be right on every count, but it is not likely that he is right about the interpretation of Einstein's equations as forbidding time travel (or that time cannot be treated as a dimension - if I understand Alex correctly). If such a limitation existed to those equations, then surely Hawking who is a brilliant general relativist that is perhaps among the most well-versed in those equations would certainly have said so.
As for your paper, I apologize but I cannot comment on it. But, I'm curious as to why your paper can say so much about the scientific understanding of time (or incorrect conception of) but you do not consider it a theory per se. Wouldn't this fact make it a theory?
Warm regards, Harv