Intercity Lines is absolutely top drawer, fully insured, yadayadayada. For a car like the old T-Bird, unless it's a 98 pt. show car, I'd probably use U-ship. I've used them 3 times in 2014 with absolutely 100% success, cheap as hell each time as well. One experience was just loading-up a car I sold for a guy in Canada, but I met the driver and he was solid.
All three times were small operators with PU trucks pulling car hauler trailers but they were all salt-of-the-earth honest type individuals and delivered what they said they would with no damage or other shenanigans.
One was my DD, bought sight-unseen from NorCal and delivered to me for $300 through u-ship. I have 2 of the drivers' numbers in my phone if you want them. PM me.
You're going to pay double at least for Intercity or other enclosed top-shelf haulers.
My DD: