Loved the paper!
You begin with, "It is often said that in general relativity time does not exist. This is because the Einstein equations generate motion in time that is a symmetry of the theory, not true time evolution."
Moving Dimensions Theory, with its simple postualte that the fourth dimension is expanding relative to the three spatial dimensions: dx4/dt=ic, provides a foundation for all of relativity; while also weaving change into the fundamental fabric of spacetime for the first time in all of relativity.
It is dangerous to talk about the "The paradox of time in quantum gravity," when quantum gravity exists neither in theory nor in practice. It would be like trying to make a science out of the paradox of the flying spaghetti monster.
You write, "The quantum theory of gravity will be spaceless, not timeless."
MDT, on the other hand, proposes that we keep space, time, physics, logic, reason, and simple postulates and equations unifying diverse *physical* phenomena, while also ridding ourselves of things that don't make sense, such as the block universe and frozen time.
You would enjoy my paper!
"In his 1912 Manuscript on Relativity, Einstein never stated that time is the fourth dimension, but rather he wrote x4 = ict. The fourth dimension is not time, but ict. Despite this, prominent physicists have oft equated time and the fourth dimension, leading to un-resolvable paradoxes and confusion regarding time's physical nature, as physicists mistakenly projected properties of the three spatial dimensions onto a time dimension, resulting in curious concepts including frozen time and block universes in which the past and future are omni-present, thusly denying free will, while implying the possibility of time travel into the past, which visitors from the future have yet to verify. Beginning with the postulate that time is an emergent phenomenon resulting from a fourth dimension expanding relative to the three spatial dimensions at the rate of c, diverse phenomena from relativity, quantum mechanics, and statistical mechanics are accounted for. Time dilation, the equivalence of mass and energy, nonlocality, wave-particle duality, and entropy are shown to arise from a common, deeper physical reality expressed with dx4/dt=ic. This postulate and equation, from which Einstein's relativity is derived, presents a fundamental model accounting for the emergence of time, the constant velocity of light, the fact that the maximum velocity is c, and the fact that c is independent of the velocity of the source, as photons are but matter surfing a fourth expanding dimension. In general relativity, Einstein showed that the dimensions themselves could bend, curve, and move. The present theory extends this principle, postulating that the fourth dimension is moving independently of the three spatial dimensions, distributing locality and fathering time. This physical model underlies and accounts for time in quantum mechanics, relativity, and statistical mechanics, as well as entropy, the universe's expansion, and time's arrows and assymetries across all realms."
Time as an Emergent Phenomenon: Traveling Back to the Heroic Age of Physics by Elliot McGucken