Free placement tattoo.

Hello! There was such a problem. You need to make a tattoo that moves freely throughout the character’s body. The mesh has 4 materials with different UVs and you need to avoid displaying seams.
We make a cylindrical projection onto the model using the VectorToRadialValue function. It uses world coordinates and object coordinates. We transform them into local coordinates that are attached relative to the pivot of the object. Since the mesh of the object during the animation shifts relative to the pivot, we also get the projection offset on the body.
Tell me, how can I solve this problem? Or maybe someone knows a more working way?
We used a pre-skinned local position, but there were problems with repeating textures (Clamp was set in the texture settings).