Control time remapping with a gradient map

I'm working on something similar.

To each composition I added a color control with a sample image.

target = thisComp.layer("yourGradientComposition");
target.sampleImage(transform.position, radius = [.5, .5], true, time)

Then I added a slider to obtain a value (from 0 to 100) of that color.

var rgbColor = effect("Color Control")("Color");
var hsl = rgbToHsl(rgbColor);
var lightness = hsl[2];
lightness * 100 

At the end, in the composition of your animation you activate the time ramping and with a linear you adjust the transition, using the value of your slider, from black (0) to white (100)

var src=effect("value")("Slider");
var f = linear(src, 10, 100, 0, 60);
framesToTime(f)

Repeat the source image with Motion Tile, apply the Time Displacment effect, create whatever gradient you need in a pre-comp and quantize it with the Mosaic effect so it lines up with the other grid. The basics take 3 minutes to set up, the rest is just endless tweaking to get the right timing and look.

Mylenium