Try Elite Transporters at 1-580-774-2690 Nina or Gary. My 68 original with 11,500 miles was transported from Arkansas to New York in May and I was extremely pleased. The person I bought the car from (Craig Whitlatch) made the arrangements with them for me. It was an enclosed trailer, cost me $1050.00. Craig has used them many times. Good luck.
I should also mention that Elite brought my car straight thru, no sitting in a depot somewhere waiting for pickup. It left Arkansas on Wednesday and got in Poughkeepsie New York Saturday morning at 9 a.m. The driver was great.
I would recommend Elite Auto Transport as first pick. I've used them on several occasions and they are very good at what they do. If they're booked up for some reason, then go with Horseless Carriage. I hope this helps and good luck with the new ride.
If it's a really nice car/show car, there is only one choice Horseless Carriage Transport. They are the factory transport for Rolls Royce, Ferrari etc. The cost is a bit more (not that much) but it is a class act. The car is fully enclosed and covered during transport. I believe It cost about $1800 to ship my car from PA to CA 4 years ago. They are based in NJ/NYarea.
I recently heard someone had their show car shipped by somone else and had the car show up with a spot rubbed through the paint across the roof.