Factory Five Racing has used Stewart Transport for years. I used them once and was satisfied. I think $1400 sounds about right for coast to coast, just call and they will give you a prompt estimate, looking at their website the contact guy is still Colin: he was there 3 years ago at least. When my car arrived I looked in the large enclosed trailer and there were some pretty expensive cars inside. The driver appeared very knowledgeable and had worked for them for years as well.
There are a lot of ways to damage a car while shipping it. Especially these cars with their limited clearance.
2006 Exige, starlight black.
2003 FFR Cobra, red with white stripes, 190RWHP
2005 FFR Cobra, blue, 290 RWHP
2000 Corvette FRC, Doug Rippie 480 HP, black
1997 Mazda Miata with nitrous, SM suspension
2002 Van's RV6, Sun N Fun Grand Champion, etc