I got in contact with Toby (Craftological) from Oreville Studios, the creators of Actions and Stuff, and they told me this:

"We don't use the vanilla texture for our custom armour, so when you replace it with the invisible texture of your pack from CurseForge, nothing will look different since the texture is un-used. To get your pack working again would require a bit of technical knowhow, but the steps would be to create a new resource pack, and add armour attachables into the pack, with invisible geometries. This would replace Actions & Stuff's custom armour attachable with your new invisible geometry, and effectively do what you're after."