Take an extra day to get here and just drive it.
I could not imagine being down here for 5-8 months without a car. I had friends that had no car and took the bus everywhere and they hated it.
Having my car down here made my experience increase ten fold I am sure. Being able to go anywhere you want , whenever you want, is a blessing in disguise. There are a million things to do down here other than Disney and I believe if you didnt bring a car, you would be mad at yourself.
Autotrain only goes from VA to FL, so I know thats not an option, but shipping a vehicle isnt really a cost effective solution. I had a vehicle shipped a similar distance and it cost about $1100 plus insurance when I was moving out of Cali.