I negotiated a value for our Jaguar that was damaged by a State Farm insured. They did not want to use the "diminished value" claim that I originally started with. They asked that I submit what I would accept and they would review and rule on my suggestions. I submitted three different alternatives and they agreed to write me a check for the full amount that I requested. No lawyer involved and I feel that they handled it very well and quickly.
I would get all of your figures together and just tell the insurance company what you would accept. Try to avoid using the "diminished value" reference and see how it goes. Remember they are supposed to get you back to where you were before the accident. Some companies are easier to deal with than others but I would think that a large company that handles commercial vehicles would just be interested in a quick settlement.