Fedex is has been the cheapest for me when shipping larger items. I have shipped grills, dash pads, bucket seats, door panels, and many other large items with no problems at all...most to board members here. It has never been to expensive. Ask Keith (lolife99) how his dash pad arrived from me.
I usually make my own boxes so they are as small as possible. I typically use newspaper to package them safely...and a lot of it. The key is to stuff it enough so te item won't slide around while not stuffing it too much that you bend the item trying to get everything in the box.