The Cartographic Polygon system - and raster overlays in general - are meant to be draped on ECEF-aligned tilesets. If yours has a local origin instead, it’s going to cause problems. Raster overlays work by projecting polygon points down (or up) onto the globe surface along the ellipsoid surface normal. But for a tileset with a local origin, this operation doesn’t make any sense until the tileset is placed on the globe. And then if the object moves (which is often the reason to use a local origin in the first place), the raster overlays would need to be recomputed.
So, my advice is to take your EPSG 27700 model and unproject it to ECEF before tiling it. This will be both easier and more accurate than trying to display a projected model on a true 3D globe.