Problem statement
While integrating one of our Spine files into our Unity project, I found that the z-order for the animations was correct, until I modified two of the materials used by this skeleton to use the "rim-light" shader I wrote. At which point the z-order for the symbols changed significantly. Using the default materials here doesn't cause this issue, and the issue also seemingly doesn't occur on another character with even more atlas pages (or at least is a lot less noticeable on this other character if it does still occur).
Here's what it looks like with our custom materials:

(Note that these characters are both part of the same Spine file/SkeletonData.)
Here's what it looks like without our "rim-light" outline shader:

I attempted to add a Sorting Group component, but it didn't seem to change the behavior at all (and indeed I already had set a sorting layer on the Skeleton component).
Each of these atlas pages are already 4096x4096 pixels, and we are hoping to optimize for PC and Mobile, so we are trying to avoid making the textures any larger than 4k. What is causing the Z-Order discrepencies and is there any way to reasonably work around this issue without resorting to a single atlas page and material for this fight?
Runtime information
We're currently using Spine Runtimes v4.2.xx, with plans to upgrade to v4.3 when it is released on the stable branch.
Any help you can provide would be great, and I can email and project files needed to reproduce this issue if requested. Thank you!