I decided to go back optimizing my terrain shader. A limitation of my initial adjustment of the CesiumDefaultTilesetShader was that the masked area stayed at 0, 0, 0 in world space.
From what I gathered in this tutorial: Waterfall Shader Breakdown | Cyanilux
I need to pass the position of the object I want the clipping mask to follow to the shader.
Looking at this thread I eventually managed to implement passing of values to material properties of loaded tiles during runtime after initially trying to do it through the Opaque Material property of the Cesium3DTileset component: Shader for Cesium World Terrain - Cesium for Unity - Cesium Community
Because I want the map table object to be fully interactable (transforming, scaling, rotating) I will look into passing the appropriate values to the shader and adapting the shader further eventually.