If you have one, a very large rubbermaid tub or two with a homemade wire mesh top works great. I've used this before to transport birds.
I simply took a piece of mesh larger than the tub, formed it into a rough 'U' shape (so the short sides of the U were wrapped around the sides of the tub) and took a pair of straps (used to attach the bikes to the car for vacation) and wrapped around the whole thing - to keep the birds from knocking the top off in mid-drive.
One thing I find VERY helpful is to use a LOT of pine bedding in the bottom of the tub. Helps to minimize odors, especially if you cannot have the window's down! Otherwise the stench is enough to knock your knickers off! Pewwwwwww.....
edited to add: if you're planning on using cardboard boxes - see if the facility will allow you to dispose of the boxes there. You DON'T want to take those stinky boxes back home! Trust me....1hr is plenty long to sniff that smell.....
Well had a great experience at the processor (Plucky Poultry in Ohio) and it was only 28.20 for 11 birds split, innards, ice and bagging. They were kind and fast, the boy who did the processing explained the process to my 5 year old who was hesitant at first to get near the building, however she did end up watching and was very intrigued.
While waiting for my turn I was able to talk with the others who were getting their poultry taken care of and they had nothing, but rave reviews. I can see why it was difficult to get an appointment, so if you use them make sure you call asap to schedule an appointment.
I use a large dog crate. You can spray it out with the water hose afterwards. Mine never see the light of day on processing day. I get them before daylight and arrive at the processor before daylight. They are hung up by the feet one at a time and I drive off. Come back 2 days later and pick them up in labeled vaccuum sealed bags.
I always leave them hole. This time I am going to have most of them cut up.