In my opinion, these paradoxes invalidate this hypothesis as a credible model of time travel.
This is the point on which we disagree. It is only this model which precludes the existence of a paradox, and as a paradox cannot exist it seems to me the only credible model.
And about mass-energy: two waves of opposite amplitude will cancel each other - this means, their energies will delete each other. What happened to that energy?
An interesting question. Its a long time since I read anything about wave interference, but I am confident that the laws of thermodynamics are obeyed.