Amadeus and I arrived safe and sound, and I think he even actually enjoyed the trip! I found a clear top for his betta cup so I could keep an eye on him while in the car, and I noticed that the places I thought would be bumpy and jostle him around didn't actually move the water much. The cup-in-cupholder idea was good, that seemed to keep him very safe and secure. I stopped every hour to check on him (mostly to check water temp), the water stayed around 78 degrees and he seemed to really enjoy looking around at everything in the car (well, what he could see from the cupholder, at least). He is currently quite happy in his one-gallon tank, very active and seemingly loving having new things to look at, and tomorrow I get to go pick up the 5-gallon to take home with me!!
The only negative part is that I broke the air stone for his UGF, however, I'm going to look at other mini-filter options at Petsmart tomorrow. I'd love for him to have a somewhat better filter than what came with the tank...