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Honestly, with a four hour drive on standard roads, I wouldn't worry about resting them or refraining from turning. Eggs shipped through the mail are tossed around, dropped, and generally abused. I used to deliver to the back room at the local post office; I've SEEN how they treat a package, regardless of whether it says 'fragile' on it. I've stood there and watched the UPS driver chucking boxes out the back of her truck toward the general vicinity of a cart ten feet away.
I would suggest that you candle the eggs, take a look at the condition of the air pockets. If they are detached or 'saddled' - two of the big problems with eggs shipped through the postal service - then rest them. Otherwise, pop them in to start cooking immediately.
As far as the heat... is there any way to set up fans near the incubator, with buckets of water in front of them? This is a fairly natural method of cooling an area off, just like hosing down the chicken run to make mud for them to play in. I do that two or three times a day, since it's averaging about 103 F. here currently, and it's the same concept as a 'misting' machine.