[waynet]

I am looking for a company that will transport one vehicle from the Villages to Connecticut and pick up a vehicle at the same address and deliver it to Florida.

[Phanatic Luvr]

Try Reliable Carriers. Gary and Paula Morrison (904) 742-6000 cell. I believe they come out of the Jacksonville area and run up and down the east coast and farther.
I believe they have been doing it for 30 some years. Nice double-decker, enclosed transport vehicle.

[mtdjed]

You could do it yourself or have a relative do it using the Autotrain both ways. Part drive part train. Probably around $1200 for train and gas/tolls.