The problem here is that you can't represent tidal deformations purely through time dilation, since they bring (parts of) objects closer together. The tl;dr is: "how does your idea explain that Earth is oblate, with objects at the two poles slightly closer together than objects on the equator but on opposite sides of the planet?" General Relativity explains this as tidal forces acting on the planet, which is in approximate hydrostatic equilibrium, but rotating. The same features explain why a measurement of the local gravity (the field strength "g") at the poles gives a higher number than at the equator. It also explains the shape of the moon in its synchronous orbit.

In General Relativity we can decompose the Riemann curvature tensor into the Weyl tensor, the Ricci tensor, and the metric tensor. The Weyl tensor encodes the squash-stretch deformation of moving objects experiencing shear, for example, a rotating spherical body deforming into an oblate spheroid, or a spherical body moving close to (including synchronously orbiting) a large mass deforming into a scalene ellipsoid. The Ricci tensor encodes the volume deformation of a body experiencing tidal forces; if we drop a ball of dust (think very loosely packed coffee grounds) onto a planet, the Ricci tensor describes the tendency of the individual dust particles to converge into a smaller volume as they each fall "straight down" on individual lines converging at the centre of the planet.

Naively, we could say that there is a clear relationship between the Ricci tensor and gravitational time dilation, since time is running slower in the direction where the individual fall paths ("geodesics") converge. However, we can make the Ricci tensor go to zero by dropping the dustball onto a planet with enormous radius, such that it's effectively flat. Similarly, ultra massive black holes have essentially no Ricci curvature just outside the horizon, while low-mass black holes have significant Ricci curvature. However, gravitational time dilation is still very strong just outside the horizon of such a massive black hole. In this way we can distinguish between spatial curvature (or if you like, length contraction) and curved time (or if you like, time dilation) in the region around massive bodies. Gravitational time dilation is not a tidal effect, but rather depends on the gravitational potential, which in General Relativity is encoded in the metric tensor.

If we orbit our dust ball very rapidly around a heavy planet, it will have substantial Weyl curvature (squashed along its axis of motion, stretched on the other two spatial axes). If the planet has a big enough radius, the Ricci tensor vanishes, leaving us with just the Weyl curvature. In that case, if we measure periodic microscopic processes ("clocks") closest to the planet and furthest from the planet, we will see that the latter are running faster than the former, and the difference is precisely that of gravitational time dilation. Again, this lets us distinguish between changes in length and changes in duration in the region around massive bodies.

Gravitational effects are the result of curved spacetime, although in special circumstances practically all of the curvature can be in the timelike axis, and in other special circumstances practically all of the curvature can be in the three spacelike axes.

I don't understand what you mean by "quantum progression".