Just saw this thread so insight might be a little late for you, but might help others. I always bring the manager/owner into the facility and let them make an estimate of material. Then there is never a question. Example, three different scrap yards bid on an estimate of 10,000 tons of metal. We took the higher bid and only ended up with 5,000 tons. They had no complaints because they did the estimate. Before the job was done we renegotiated with them to avoid having to separate cast, from steel, from non ferrous. They set the prices based on their inspection. We came out smelling like a rose on this deal.

You asked the question if you can get better prices for the amount. Yes you can, but you have to let each scrap yard know you are taking bids from others. You have a nice project going, keep it up.