Issue with Sleeves on Custom Dyable Shirt

[Delatrix]

Hello! I am trying to make a Content Patcher mod that (among other things) adds a new shirt to the game, and I am having some trouble with the way sleeves behave.

I finally managed to get the sleeves to persist the pixels I wanted, but then when I tried to add a dye overlay, I end up with the attached image. It looks like when the dye gets applied, it is properly coloring the overlay on the main shirt body, but the sleeves are staying the same white as the overlay...

I know as a last-ditch effort I can always make each shirt color I want individually and not worry about making it dyable, but I would really like to allow the player to customize it.

I'm hoping someone else has encountered this and found a solution? Ideally I want to avoid adding more mod dependencies if I can, so I'd rather not have to download something like FashionSense just to get this one shirt working...

The shirt's texture file is below:

And here is an example of this object's item definition entry:

"{{ModId}}_CoolFuturisticShirt": {
  "Name": "{{ModId}}_CoolFuturisticShirt",
  "DisplayName": "Future Shirt",
  "Description": "A cool shirt with LEDs adorning it.",
  "Price": 3000,
  "Texture": "Mods\\MyModName\\Objects\\CoolShirts",
  "SpriteIndex": 0,
  "HasSleeves": true,
  "CanBeDyed": true,
  "DefaultColor": "Red",
  "IsPrismatic": false,
  "CanChooseDuringCharacterCustomization": false,
  "CustomFields": {}
},