How about a somewhat different approach;
It would seem logical that our sequential process of perception is a consequence of being mobile organisms and having to navigate our environment. Then as humanity, culture and civilization are primordially narrative based.
So our perception of time is as the point of the present, moving past to future. Which physics codifies as measures of duration.
Logically though, it is change turning future to past. Tomorrow becomes yesterday, because the earth turns. Duration is the present, as the events unfold.
There can be no literal dimension of time, because the past is consumed by the present, to inform and drive it. Causality and conservation of energy. Cause becomes effect.
Energy is "conserved," because it is what is present, rather than a point between past and future.
It creates time, as well as temperature, pressure, color, sound. Frequencies and amplitudes. Time is frequency, events are amplitude.
So energy, as process and present, goes past to future, while the patterns generated go future to past.
In terms of a wave, the energy drives it, as it is passing through, while the fluctuations rise and fall.
As with a factory, the product goes start to finish, while the production line goes the other way, consuming material and expelling product. As lives go birth to death, while life moves onto the next generation, shedding the old.
Consciousness goes past to future, while the perceptions, emotions and thoughts go future to past. Though it is the digestive, respiratory and circulatory systems processing the energy, while the central nervous system sorts and orders the information.
Which creates this impulse to explain reality in terms of how it is defined, rather than what drives it.
Consider that civilization is a collective process, which requires common rules, regulations and measurements, so the idea of a universal flow of time is essential to a functioning society, but different clocks can run at different rates simply because they are separate actions. Think metabolism.
A singular organism, even if it is a hive, has to synchronize its actions and clocks, while an ecosystem has to harmonize its actions, so they balance out and fill the space.
Time is asymmetric, because it is a measure of action and action is inertial. The earth only turns one direction.
Ideal gas laws correlate volume with temperature and pressure, but we don't refer to them as the 5th and 6th dimensions of space, becuse they are only foundational to our emotions and bodily functions, not the sequence of thought.
The future cannot be determined, because the process of determination can only occur as the present. The total input into any event cannot be known prior to its occurence, as the required omniscient omniscience is an oxymoron, as knowledge is a function of context and subjectivity, otherwise it is a whiteout.
While free will is also an oxymoron, as a will free of cause would be equally free of effect and the premise of will is to affect. We are a small part of nature's process of selection.
Given consciousness functions equivalent to an energy and it's the energy that is causal, we are driven by our desires and appetites and marginally steered by our judgements.
I could go on with this, given much of modern physics is based on the premise of "It from bit," but I'll leave it as something to consider.
