To clarify, I had an unexplicable issue, where the crafting recipes did not work. The book of knowledge is crafted, but was supposed to be replaced by the afformentioned armor item. This did not happen, even though I couldn't find mistakes in my code. Still not knowing why that was, I rewrote these parts and now it works!
I have some working armors now, and will try to get custom textures using CustomModelData. I have done some attempts, but have not succeeded quite yet.
Thanks for the nice responses!