Pixels skew vertically as object scales horizontally

I asked this before but it was magically marked as answered when it was clearly not answered, so I must ask again.

I don't trust me to describe this well, so here's a video of it.

There are two 'health bars.' They both behave this same way:

When the object's scale is 1.0, 2.0, 4.0, etc, flickering happens. Otherwise, there is no flicker and it looks exactly as expected. The game requires the object to be displayed at a scale of 1.0

The bars change from red to green through a basic localScale.x = p, localScale.x = (1-p) for the green and red sides. I first tried just resetting the mesh vertices, but that had the same behaviour.

Upon closer inspection (you can see this in the video), the texture's pixels skew vertically, both ways - showing the bottom row of pixels from the sprites above and below this one in the atlas (!!), as well as making artifacts along the bright white line of the visible sprite.

This is not related to Z-fighting. The sprites for the bars are 16x16 blocks of a 2048x2048 texture, and every vertical column in the sprite is identical - some of the columns are being rendered one pixel above or below where they should be. The mesh isn't skewed, just which pixels are displayed.

As an experiment, I built a coroutine to loop over all sprites and set their localScale to Mathf.Sin(Time.time) (so everything squishes and expands over and over). Every single sprite suffers from this resize-flicker.

Is there a workaround for this that doesn't involve losing pixel perfection? Another way to implement accurate health bars with sprites, perhaps?

Here's a picture of the actual mesh construction going on. Can't render the actual sprites in pause mode 'cause my setup doesn't do the right stuff to the mesh: