Are there any rabbit shows in the area in the near future? Some breeders are willing to transport for a small fee of about $10-25 per carrier. Depending on the distance and timing, it may take a day or 2 to get there. Try contacting breeder clubs in the area (both Iowa and Atlanta) to see if anything can be worked out.
Some rescues (dog, cat and other species) do travel to pick up or drop off animals. They may be willing to transport your rabbits for a small donation.
How are you getting there? While buses usually don't allow pets (you can check), trains might. You might also be able to find someone going that way and you could offer to split the costs. If you drive, you could rent a car, but the hotels can be expensive.
It would be tricky to do a trip for $200. Most hotels around here at $100 a night and up. You could try motels and not tell them you have a rabbit (you would need to keep the place really clean). Gas is expensive right now and that doesn't help.
