I was going to reply with a similar solution to Jason's. Last year I was in the middle of moving into my new house when I discovered one of my females dropped a very late clutch.
Pack the egg box with something soft (moss or paper towels work well) to prevent the eggs from rolling. As far as keeping them in the incubator while you drive, I really wouldn't recommend it unless you can somehow make sure that the egg box won't slide around within the incubator.
Instead, plug in the incubator like you already planned on doing. This will eliminate the warm up time once you reach your destination. Then, get a cardboard box (or an appropriately sized Rubbermaid tub) that is big enough to place your egg box into it with some "wiggle room". Pack the free space around the egg box with towels or some other material that will hold the box in place. The time it takes you to reach the school (30 minutes) shouldn't impact the eggs too much. The extra "padding" in the egg box along with the cardboard box and it's padding will help to insulate the egg box a little bit. Just be sure that you don't have your A/C blowing directly onto the box.
Even if your eggs were to experience a 10-15 degree drop in temperature during your trip they should be just fine. Many people have had power outages or other things go wrong while incubating that have resulted in much lower temperatures for a much longer duration and still had viable eggs.
Like I said, your main concern is making sure the eggs don't roll. If they are stuck together in an egg-mass you should be fine.
Good luck!
P.S. THANK YOU SO MUCH for sharing this experience with the kids you teach! Education is the VERY BEST thing for this hobby/industry. It not only alleviates fears and phobias but also does away with many of the misconceptions concerning reptiles in general and snakes in particular that some of those kids may be hearing from their family and friends! Again, "Thank you!"
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Stay United!

I'm still not sure if it's weird that my best friend is a two year old boa named Ronin. He's quiet, non-judgemental and listens... what more could you want?