This is interesting. I, too, have thought a lot about time. I agree with you that time in physics does not exist, but I reach a different conclusion. The failure of physics to accommodate time does not mean that time does not exist, it means that physics, as it is currently interpreted, is incomplete. The thermodynamic arrow of time is real, and the arrow of evolving complexity is real. They are not recognized by prevailing interpretations of quantum mechanics or general relativity, but they are essential to probably all other sciences and they are real. Physics will recognize time as real as soon as it lets go of its unfounded assumption of non-contextuality. Physics can then recognize properties, like entropy, as objective contextual properties of state. Entropy’s objective increase as a measure of real time.