"The transport company, DAS, told me nothing can be in the truck."

Keep checking into it. That's what the vendor told me too but when they contracted with the actual transporter, he had no issue with 4 wheel/tires in the back. Let them know that the item (although large) weighs less than 30 lbs & that the transporter will not be responsible for that item's condition upon arrival. They shouldn't have any issues with that.