Flat rate is safer, because a weight based quote can move on you at the scale and you find out after the truck is loaded, which is the worst possible moment to be negotiating. Ask for a binding number against a written inventory. The kiln should be listed separately, it is heavy and awkward and you do not want it treated as a surprise. We used
movers from California to Texas with a locked price and the number held. Get the delivery window in writing too, since long distance loads share trucks and a vague window is where the frustrating stories start. Photograph the tools and the kiln before loading, claims on specialty items go far more smoothly with dated pictures.