Ok those screenshots and description help a lot! Here's some things to try:
In the inspector try disabling ZWrite. This is basically there just to make it so Ultra shader outlines don't go over the previous letter, but if your outlines are thin enough you may as well disable it, it can *sometimes* cause something like this to happen if text is is a 3D space like this, rather than being on a UI. I feel like this shouldn't be happening with ZWrite on though, so if this solves it I'll look into how to prevent it from being a problem in the first place.
I'd also check out the rendering order of those objects in the background, is their render queue above 3000? You can try changing the render queue value on STM's material settings to something higher!
Do you get a result similar to what you want when using the Universal shader (plain version with out outline) then adding an outline through STMMaskableGraphic? That's also an option for rendering outline effects now, too!