CC Ball Action looks pixelated when I scale up — any fix?

As OP pointed out, CC Ball Action maxes out with a Grid Spacing of 50, so while this is a clever technique, it hits a wall pretty quickly. The CC Sphere effect can mimic the look of a single sphere, but I don't think you'll get this same ease of movement or correct overlapping, as you're ultimately dealing with standard 2d layering.

This would be relatively easy to recreate by importing a simple 3d sphere - that's probably how I'd approach it for the size you're looking for. It'll require a bit more knowledge about 3d and expressions, but still rather entry-level versions of each.

You'd be able to create a sphere quickly with Cinema 4D Lite (included with your AE install), or honestly, you could also create it in Adobe Illustrator, since they added some limited 3d capabilities (and the ability to export as a model). Save it as an OBJ or GLTF and you'll be able to import directly into AE. More complex than the example you posted, but doable. 

It'd be easiest to do the coloring directly on the models (outside of AE), because you can't apply effects direcly to imported 3d models, but you *can* apply colors via effects, using a second layer and effects like Calculations. (Again, more complex.)

In this example, I created the spheres in Illustrator, applying the color there before exporting them. 

I imported and arranged the spheres, then applied the Position wiggle to each (using the same settings applied to Scatter in the tutorial). I created a Null, enabled 3D and parented all three spheres to it - this will be our tumbling rotation point.

Hopefully this helps get you moving in the right direction - let me know if you have questions!