Here is a thought to consider;
As mobile organisms, the fact we experience our world as a sequence of perceptions would be a logical consequence of having to navigate it, so our concept of time is as the point of the present, moving past to future. Physics codifies it as measures of duration, correlating them with measures of distance to create the geometry of spacetime.
The reality is that change turns future to past. Tomorrow becomes yesterday, because the earth turns. Duration is the present, as the events coalesce and dissolve. Potential>actual>residual.
There is 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.
Different clocks can run at different rates simply because they are separate actions. Think metabolism.
That human culture is about synchronizing society into a larger metaorganism, based on the same rules, measures, etc, it might seem there should be some universal, Newtonian flow of time, but it's rabbit time, turtle time, etc. That nature is so diverse and yet so integrated, is because everything doesn't march to the beat of the same drummer. Multicultural, not monocultural.
Time is asymmetric, because it is a measure of action and action is inertial. The earth only turns one direction. Entropy is a second order effect and not what is directly measured.
Energy is "conserved," because it is manifesting the present, creating time, as well as temperature, pressure, color and sound. Time is frequency, events are amplitude.
Ideal gas laws correlate volume with temperature and pressure, which are as foundational to our emotions and bodily functions, as sequence is to thought, but we don't try modeling them as extensions/dimensions of space. Only measurable effects of the activity occurring in space, like time really is.
As present, energy goes past to future, while the patterns generated go future to past. Energy drives the wave, while the fluctuations rise and fall. No tiny strings necessary.
Consciousness also goes past to future, while the perceptions, emotions and thoughts giving it form and structure go future to past. Though it is the digestive, respiratory and circulatory systems processing the energy, feeding the flame, while the central nervous system sorts through the information, signals from the noise.
So now think of how physics conducts itself, that you have so clearly and eloquently explained. Entirely in terms of the information it can extract. Yet there seems to be some missing void. It's like all this information really is just shadows on the wall. Products of the light.
Yet galaxies are energy radiating out, as structure coalesces in.
Consider that waves, as form, will tend to synchronize, as it's a path of least resistance. Which is consequently centripetal. While the energy, of itself, radiates out. Which is its path of least resistance. So both are entropic, but going in opposite directions. One coalescing toward equilibrium, while the other radiates toward infinity. Like the number line, from zero to infinity. Though neither quite reaching, just feeding back, in cosmic convection cycles.
Nodes and networks, organisms and ecosystems, particles and fields.