Some bike shops apparently will pack for shipping. I'm not sure who carries the liability for their shipping though.
I haven't shipped any bikes, but I've received various bikes and components.
I wouldn't build a wooden crate. People have been shipping bikes in cardboard boxes for eons.
It only takes a few seconds to remove the rear derailleur. Much better than having it hanging down.
Bubble wrap & foam is your friend. Also consider pipe insulation. Wrap EVERYTHING. When I've bought well packed frames, I've been happy that the fork was tie wrapped to the frame... Best to minimize loose parts bouncing around the box. You probably don't want to remove the fork, but I'd control the interaction between wheels and other parts.
I wouldn't add support to the corners of the box. They should be stiff enough. But, most frames and forks I have bought came with some kind of support between the front and rear dropouts of the bike.