Putting 4 birds per box in an eight square foot area is plenty of room. Make sure you cut a lot of about 1" air holes in the top and around the upper sides of the boxes. They will build up a lot of heat in those boxes and you actually don't want that. Put some pine shavings in the bottoms of the boxes to absorb waste.
They will NOT enjoy the ride. They will be terrified. I transported three 7 month old pullets in a small dog crate of about 2.2 square feet for a 1.5 hour trip. They never made a peep in the back of the car. They made the journey just fine and are now some of the best birds in my flock.
I would advise that you carefully examine each bird prior to putting her in the box. You will be looking for signs of disease or parasites. Look at the vents, under wings for signs of mites or lice. Look at eyes and nares and comb color and over all feather condition. They should look bright, clear and alert with good plumage.
When you get home and remove them from the boxes, exam them again. You are looking for injury this time.
I would suggest giving them one water container with just fresh plain water and a second with electrolytes for the first three days. Also give them some Poultry Nutri-drench or Rooster Booster in their feed for the first three days as well to help them recover from the stress of the move.
Good luck and congratulations on the new flock!