It's a great technique. I tried implementations of this same trick in the past but never got it to work this well.
Looked at your blog article's PSD, finally. (using Photoshop CC 2014)
Smoothing out a pixel art workflow in Photoshop always interests me so I messed around a little:
Got 3 set of layers, for 3 different dynamically indexed elements in the canvas - two mountain ranges and the sky bg.
DITHER
Used Fill Layers set to Fill 0%, used Pattern Overlay in Layer Style.
Just a preference, really.
I find handling the dither pattern overlay easier this way.
Also, you can't accidentally draw on it and have any effect since its Fill is set to 0%.
I made sure to use the Position Lock (top of Layer Panel) for all Dither layers so I can click through them, since I leave my Move Tool's Auto-Select on all the time.
If you want to selectively dither only certain parts, use a Layer Mask on the Fill Layer. Use multiple selectively masked dither layers each using a different dither pattern.
ADJUSTMENT LAYERS MASKING
Rather than mask the indexing adjustment layers to one layer, I've masked them to groups that can contain other layers and layer groups.
This allows composite layers to all live in one layer group, getting the indexing effects. No need to commit to merging layers together - like the foreground figure in
your youtube video. Multiple sets of indexed elements all in one PSD.
Notice all the cloud bg spiral Smart Objects (made into SO's just so I can rotate them freely) inside the "spiral moons" layer group. That layer group's blend mode is set to Lighten, affecting all layers within, without affecting the "clouds" layer.
Infinite possibilities.
LAYER COLORS
Using a Layer Panel color-coding standard can help when working with a PSD with lots of layers.
I have my own little meanings I've attached to the available colors.
Main goal is making things easier/faster to find.
And I wanted to find a way to eliminate all alpha transparency in a pixely way.

Using the Dissolve blend mode is all I really came up with. Always ugly, though.
But it does allow you to draw uninhibited with AA tools on a non transparency locked layer - all feathered transparency gets completely removed.
Maybe it's only useful as a safeguard - when using it, you know there won't be any accidental alpha blending going on (if you don't want it).
The motion paths of this flame are too large to pull off an 8 - i'd have to tone back the animation quite a bit and make it feel a lot higher-frequency in detail/motion.
You're saying you'd have to use a much smaller patterns so the motion actually loops quicker, right?
Tween the pattern on the right moving over, and blending into, an underlying texture.

Once you've moved the smaller pattern a distance equal to the tile's dimensions you have a complete loop.
Just thinking out loud . . . visually . . . in a forum.
Anyway, super cool.
Thanks for posting your technique and opening my eyes to this.