I think it is best if you move them in crates, so they don't get bounced around too much. When you take rest stops, maybe you can let them loose in the trailer to eat, drink, poo, before locking them back up.
Some people bring a covered wire exercise pen ( for dogs) so they can spread their wings and do their business outside. You would have to be careful that they don't get lose when transferring them to the pen and back.- maybe just do a few at a time. Is there a way they can get some ventilation in the trailer,? .I can't picture what it looks like, and what the temperature would be like at that time of the year. You can also put a radio with them and the music may keep them from stressing - unless it's heavy metal.
I've heard of other folks packing them(in crates) in their car, so they can control the heat/ cooling and ventilation - also keep a good look at them to know what is going on. Hope some of this helps.