It certainly sounds like a GREAT idea and really great pricing but we have a DOG and a CAT that has to travel with us. The cat is young and could handle being in a cat carrier in a "baggage car" but our dog is old and very "spoiled" and probably would not make the journey in a crate in a baggage car !! (That is if they even allow PETS on trains ??)
Floridawen, Like Jon and your family member, I would also be willing to drive the car up to CT for you (I live in NYC). Another possibility is to try to get a trustworthy college student or other person near you to drive the car to CT. When I was a college student, I once drove a car from NY to Washington State. The car's owner merely provided the car in exchange --- no other reimbursement whatsoever. There used to be services that put car owners and drivers together. Don't know if there are still any. Issue for you is finding a driver to satisfy the trustworthy criterion. Anyway, good luck.
What about getting a trusted family member to fly down to Florida (at your expense)? Put them up for a week or so in your home, so they have a vacation in the sun and on the beach (if you're near one). Being a family member, they'd stay with you at no cost to you except food. Then, being a family member, they'd drive the car up north for free. You'd pay gas, and overnight lodging.
Under different circumstances (my Sister-In-Law has a serious medical condition and goes to hospital every few days for Dialyses) my Brother would probably drive my vehicle up for me, but with two teenagers in school and his Wife needing daily attention it would not work out for him. I also want to keep down the miles / wear-and-tear of a FL to CT journey so putting the vehicle in a carrier, preferably "covered" would be the "best" choice at this time. My other good friend in Connecticut just blew all his three weeks vacation with his Wife, visiting his "in-laws" in Brazil. He might have done the drive if he had any "time" left. I think it still is best at this point to have the CR-V "transported" even if it cost me around $1200 !!
Well, good luck, then. I hope the move goes well. Unfortunately, I know nothing about carriers and truckers, so I cannot offer any advice regarding a reliable one. I moved from Fargo to Spokane about two and a half years ago, and it was a stressful time, though all went smoothly. I hired a mover for my things, and drove my Prius.
I've been calling quite a few vehicle transport places all over the U.S., many of the names I got from a web site that "rated" them highly to poorly and posted comments from customers, satisfied or unsatisfied. Seems that they all "talk-the-talk" NOW and promise excellent care of your vehicle and prompt delivery which makes it a decision based quite a lot on people's reccomendations.